##############ECHO OF PROBLEM################# ##############temp/sing3_backpostode.ode################# diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=20; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=c(-0.7); x_end=c(-2.0); array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_type_given_pole=1; array_given_rad_poles[1][1]=c(0.0); array_given_rad_poles[1][2]=c(0.0); array_given_ord_poles[1][1]=c(2.0); array_given_ord_poles[1][2]=c(0.0); // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=8; glob_max_minutes=(3.0); glob_subiter_method=3; glob_max_iter=100000; glob_upper_ratio_limit=c(1.000001); glob_lower_ratio_limit=c(0.999999); glob_look_poles=true; glob_h=c(0.001); glob_display_interval=c(0.01); // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(c(1.0)/c(x)/c(x)); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion TOP MAIN SOLVE Loop x[1] = -0.701 y[1] (closed_form) = 2.03499789377718 y[1] (numeric) = 2.03499789377718 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.701 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.701 Order of pole (three term test) = 3.28e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.702 y[1] (closed_form) = 2.029204308406588 y[1] (numeric) = 2.029204308406588 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.702 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.702 Order of pole (three term test) = 3.423e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.703 y[1] (closed_form) = 2.023435429140303 y[1] (numeric) = 2.023435429140303 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 14 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.703 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.703 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.704 y[1] (closed_form) = 2.01769111570248 y[1] (numeric) = 2.01769111570248 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.704 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.704 Order of pole (three term test) = 1.118e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.705 y[1] (closed_form) = 2.011971228811428 y[1] (numeric) = 2.011971228811428 absolute error = 4.440892098500626e-16 relative error = 2.207234395257274e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.705 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.705 Order of pole (three term test) = 3.89e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.706 y[1] (closed_form) = 2.006275630171176 y[1] (numeric) = 2.006275630171176 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.706 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.706 Order of pole (three term test) = 8.118e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.707 y[1] (closed_form) = 2.000604182463104 y[1] (numeric) = 2.000604182463104 absolute error = 4.440892098500626e-16 relative error = 2.21977547454344e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.707 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.707 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.708 y[1] (closed_form) = 1.994956749337675 y[1] (numeric) = 1.994956749337675 absolute error = 2.220446049250313e-16 relative error = 1.113029668431409e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.708 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.708 Order of pole (three term test) = 4.419e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.709 y[1] (closed_form) = 1.989333195406232 y[1] (numeric) = 1.989333195406232 absolute error = 2.220446049250313e-16 relative error = 1.116176040483197e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.709 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.709 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.71 y[1] (closed_form) = 1.983733386232891 y[1] (numeric) = 1.983733386232891 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.71 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.71 Order of pole (three term test) = 2.404e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.711 y[1] (closed_form) = 1.978157188326499 y[1] (numeric) = 1.978157188326499 absolute error = 2.220446049250313e-16 relative error = 1.122482107263068e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.711 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.711 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.712 y[1] (closed_form) = 1.972604469132685 y[1] (numeric) = 1.972604469132685 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.712 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.712 Order of pole (three term test) = 2.616e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.713 y[1] (closed_form) = 1.967075097025979 y[1] (numeric) = 1.967075097025979 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.713 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.713 Order of pole (three term test) = 2.729e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.714 y[1] (closed_form) = 1.961568941302011 y[1] (numeric) = 1.961568941302011 absolute error = 2.220446049250313e-16 relative error = 1.131974514123613e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.714 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.714 Order of pole (three term test) = 2.846e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.715 y[1] (closed_form) = 1.956085872169788 y[1] (numeric) = 1.956085872169788 absolute error = 2.220446049250313e-16 relative error = 1.135147531527991e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.715 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.715 Order of pole (three term test) = 2.968e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.716 y[1] (closed_form) = 1.950625760744047 y[1] (numeric) = 1.950625760744047 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.716 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.716 Order of pole (three term test) = 3.095e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.717 y[1] (closed_form) = 1.945188479037677 y[1] (numeric) = 1.945188479037676 absolute error = 2.220446049250313e-16 relative error = 1.141506889013044e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.717 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.717 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.718 y[1] (closed_form) = 1.939773899954222 y[1] (numeric) = 1.939773899954221 absolute error = 2.220446049250313e-16 relative error = 1.144693229093718e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.718 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.718 Order of pole (three term test) = 6.73e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.719 y[1] (closed_form) = 1.934381897280453 y[1] (numeric) = 1.934381897280453 absolute error = 2.220446049250313e-16 relative error = 1.147884010066491e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.719 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.719 Order of pole (three term test) = 3.509e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.72 y[1] (closed_form) = 1.929012345679012 y[1] (numeric) = 1.929012345679012 absolute error = 0 relative error = 0 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.72 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.72 Order of pole (three term test) = 3.658e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.721 y[1] (closed_form) = 1.923665120681131 y[1] (numeric) = 1.923665120681131 absolute error = 2.220446049250313e-16 relative error = 1.154278894688332e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.721 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.721 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.722 y[1] (closed_form) = 1.918340098679415 y[1] (numeric) = 1.918340098679415 absolute error = 2.220446049250313e-16 relative error = 1.1574829983374e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.722 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.722 Order of pole (three term test) = 3.975e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.723 y[1] (closed_form) = 1.913037156920699 y[1] (numeric) = 1.913037156920699 absolute error = 2.220446049250313e-16 relative error = 1.160691542878567e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.723 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.723 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.724 y[1] (closed_form) = 1.907756173498978 y[1] (numeric) = 1.907756173498977 absolute error = 4.440892098500626e-16 relative error = 2.327809056623664e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.724 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.724 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.725 y[1] (closed_form) = 1.902497027348395 y[1] (numeric) = 1.902497027348395 absolute error = 4.440892098500626e-16 relative error = 2.334243909274391e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.725 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.725 Order of pole (three term test) = 4.502e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.726 y[1] (closed_form) = 1.897259598236308 y[1] (numeric) = 1.897259598236307 absolute error = 4.440892098500626e-16 relative error = 2.340687643709316e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.726 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.726 Order of pole (three term test) = 2.346e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.727 y[1] (closed_form) = 1.892043766756413 y[1] (numeric) = 1.892043766756412 absolute error = 4.440892098500626e-16 relative error = 2.347140259928437e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.727 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.727 Order of pole (three term test) = 4.89e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.728 y[1] (closed_form) = 1.886849414321942 y[1] (numeric) = 1.886849414321941 absolute error = 4.440892098500626e-16 relative error = 2.353601757931756e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.728 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.728 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.729 y[1] (closed_form) = 1.881676423158921 y[1] (numeric) = 1.88167642315892 absolute error = 6.661338147750939e-16 relative error = 3.540108206578907e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.729 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.729 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.73 y[1] (closed_form) = 1.876524676299493 y[1] (numeric) = 1.876524676299493 absolute error = 6.661338147750939e-16 relative error = 3.549827098936476e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.73 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.73 Order of pole (three term test) = 5.533e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.731 y[1] (closed_form) = 1.87139405757531 y[1] (numeric) = 1.871394057575309 absolute error = 8.881784197001252e-16 relative error = 4.746079085293785e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.731 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.731 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.732 y[1] (closed_form) = 1.866284451610977 y[1] (numeric) = 1.866284451610976 absolute error = 6.661338147750939e-16 relative error = 3.569304851680499e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.732 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.732 Order of pole (three term test) = 6.006e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.733 y[1] (closed_form) = 1.861195743817573 y[1] (numeric) = 1.861195743817572 absolute error = 6.661338147750939e-16 relative error = 3.579063712066954e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.733 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.733 Order of pole (three term test) = 3.129e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.734 y[1] (closed_form) = 1.856127820386223 y[1] (numeric) = 1.856127820386222 absolute error = 8.881784197001252e-16 relative error = 4.785114526839606e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.734 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.734 Order of pole (three term test) = 6.519e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.735 y[1] (closed_form) = 1.851080568281734 y[1] (numeric) = 1.851080568281734 absolute error = 6.661338147750939e-16 relative error = 3.598621400868751e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.735 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.735 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.736 y[1] (closed_form) = 1.846053875236295 y[1] (numeric) = 1.846053875236294 absolute error = 8.881784197001252e-16 relative error = 4.81122697237879e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.736 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.736 Order of pole (three term test) = 3.537e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.737 y[1] (closed_form) = 1.841047629743229 y[1] (numeric) = 1.841047629743228 absolute error = 1.110223024625157e-15 relative error = 6.030387300626216e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.737 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.737 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.738 y[1] (closed_form) = 1.836061721050815 y[1] (numeric) = 1.836061721050814 absolute error = 1.110223024625157e-15 relative error = 6.046763090239438e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.738 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.738 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.739 y[1] (closed_form) = 1.831096039156158 y[1] (numeric) = 1.831096039156157 absolute error = 8.881784197001252e-16 relative error = 4.850528867450521e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.739 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.739 Order of pole (three term test) = 3.996e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.74 y[1] (closed_form) = 1.826150474799124 y[1] (numeric) = 1.826150474799123 absolute error = 8.881784197001252e-16 relative error = 4.863665026277886e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.74 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.74 Order of pole (three term test) = 8.322e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.741 y[1] (closed_form) = 1.821224919456328 y[1] (numeric) = 1.821224919456327 absolute error = 1.110223024625157e-15 relative error = 6.096023685842055e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.741 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.741 Order of pole (three term test) = 4.333e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.742 y[1] (closed_form) = 1.816319265335184 y[1] (numeric) = 1.816319265335183 absolute error = 8.881784197001252e-16 relative error = 4.889990634637797e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.742 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.742 Order of pole (three term test) = 9.024e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.743 y[1] (closed_form) = 1.811433405368002 y[1] (numeric) = 1.811433405368001 absolute error = 6.661338147750939e-16 relative error = 3.677385063127758e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.743 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.743 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.744 y[1] (closed_form) = 1.806567233206151 y[1] (numeric) = 1.80656723320615 absolute error = 6.661338147750939e-16 relative error = 3.687290472953464e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.744 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.744 Order of pole (three term test) = 4.891e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.745 y[1] (closed_form) = 1.80172064321427 y[1] (numeric) = 1.801720643214269 absolute error = 8.881784197001252e-16 relative error = 4.92961227394062e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.745 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.745 Order of pole (three term test) = 2.546e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.746 y[1] (closed_form) = 1.796893530464533 y[1] (numeric) = 1.796893530464532 absolute error = 1.110223024625157e-15 relative error = 6.178568767722936e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.746 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.746 Order of pole (three term test) = 5.302e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.747 y[1] (closed_form) = 1.792085790730974 y[1] (numeric) = 1.792085790730973 absolute error = 1.110223024625157e-15 relative error = 6.19514439748059e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.747 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.747 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.748 y[1] (closed_form) = 1.787297320483857 y[1] (numeric) = 1.787297320483856 absolute error = 1.110223024625157e-15 relative error = 6.211742231698736e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.748 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.748 Order of pole (three term test) = 5.745e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.749 y[1] (closed_form) = 1.782528016884105 y[1] (numeric) = 1.782528016884104 absolute error = 1.110223024625157e-15 relative error = 6.228362270377374e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.749 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.749 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.75 y[1] (closed_form) = 1.777777777777778 y[1] (numeric) = 1.777777777777777 absolute error = 1.110223024625157e-15 relative error = 6.245004513516506e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.75 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.75 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.751 y[1] (closed_form) = 1.7730465016906 y[1] (numeric) = 1.773046501690599 absolute error = 1.554312234475219e-15 relative error = 8.76633654556258e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.751 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.751 Order of pole (three term test) = 6.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.752 y[1] (closed_form) = 1.768334087822544 y[1] (numeric) = 1.768334087822543 absolute error = 1.332267629550188e-15 relative error = 7.534026735811494e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.752 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.752 Order of pole (three term test) = 6.742e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.753 y[1] (closed_form) = 1.763640436042461 y[1] (numeric) = 1.76364043604246 absolute error = 1.332267629550188e-15 relative error = 7.554077363636225e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.753 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.753 Order of pole (three term test) = 3.508e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.754 y[1] (closed_form) = 1.758965446882761 y[1] (numeric) = 1.75896544688276 absolute error = 1.332267629550188e-15 relative error = 7.574154636813546e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.754 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.754 Order of pole (three term test) = 7.301e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.755 y[1] (closed_form) = 1.754309021534143 y[1] (numeric) = 1.754309021534142 absolute error = 1.77635683940025e-15 relative error = 1.012567807379128e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.755 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.755 Order of pole (three term test) = 7.597e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.756 y[1] (closed_form) = 1.749671061840374 y[1] (numeric) = 1.749671061840372 absolute error = 1.77635683940025e-15 relative error = 1.015251882563462e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.756 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.756 Order of pole (three term test) = 3.952e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.757 y[1] (closed_form) = 1.745051470293116 y[1] (numeric) = 1.745051470293115 absolute error = 1.77635683940025e-15 relative error = 1.017939510461474e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.757 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.757 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.758 y[1] (closed_form) = 1.740450150026803 y[1] (numeric) = 1.740450150026801 absolute error = 1.554312234475219e-15 relative error = 8.930518546890199e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.758 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.758 Order of pole (three term test) = 4.278e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.759 y[1] (closed_form) = 1.735867004813559 y[1] (numeric) = 1.735867004813558 absolute error = 1.554312234475219e-15 relative error = 8.954097463487188e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.759 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.759 Order of pole (three term test) = 4.451e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.76 y[1] (closed_form) = 1.731301939058172 y[1] (numeric) = 1.73130193905817 absolute error = 1.77635683940025e-15 relative error = 1.026023710437585e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.76 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.76 Order of pole (three term test) = 4.63e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.761 y[1] (closed_form) = 1.726754857793104 y[1] (numeric) = 1.726754857793102 absolute error = 1.554312234475219e-15 relative error = 9.001348555415234e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.761 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.761 Order of pole (three term test) = 7.225e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.762 y[1] (closed_form) = 1.722225666673556 y[1] (numeric) = 1.722225666673554 absolute error = 1.77635683940025e-15 relative error = 1.031430940656719e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.762 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.762 Order of pole (three term test) = 5.01e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.763 y[1] (closed_form) = 1.717714271972571 y[1] (numeric) = 1.71771427197257 absolute error = 1.554312234475219e-15 relative error = 9.04872399232204e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.763 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.763 Order of pole (three term test) = 5.211e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.764 y[1] (closed_form) = 1.71322058057619 y[1] (numeric) = 1.713220580576189 absolute error = 1.554312234475219e-15 relative error = 9.072458340142476e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.764 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.764 Order of pole (three term test) = 2.71e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.765 y[1] (closed_form) = 1.708744499978641 y[1] (numeric) = 1.708744499978639 absolute error = 1.77635683940025e-15 relative error = 1.039568431338012e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.765 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.765 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.766 y[1] (closed_form) = 1.704285938277581 y[1] (numeric) = 1.704285938277579 absolute error = 1.77635683940025e-15 relative error = 1.042288033659133e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.766 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.766 Order of pole (three term test) = 2.931e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.767 y[1] (closed_form) = 1.699844804169379 y[1] (numeric) = 1.699844804169378 absolute error = 1.554312234475219e-15 relative error = 9.143847901071922e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.767 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.767 Order of pole (three term test) = 3.048e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.768 y[1] (closed_form) = 1.695421006944444 y[1] (numeric) = 1.695421006944443 absolute error = 1.554312234475219e-15 relative error = 9.167706593871117e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.768 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.768 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.769 y[1] (closed_form) = 1.691014456482588 y[1] (numeric) = 1.691014456482587 absolute error = 1.332267629550188e-15 relative error = 7.878511176784287e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.769 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.769 Order of pole (three term test) = 9.888e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.77 y[1] (closed_form) = 1.68662506324844 y[1] (numeric) = 1.686625063248438 absolute error = 1.554312234475219e-15 relative error = 9.215517238203575e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.77 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.77 Order of pole (three term test) = 3.427e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.771 y[1] (closed_form) = 1.682252738286895 y[1] (numeric) = 1.682252738286893 absolute error = 1.554312234475219e-15 relative error = 9.239469189736837e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.771 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.771 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.772 y[1] (closed_form) = 1.67789739321861 y[1] (numeric) = 1.677897393218608 absolute error = 1.554312234475219e-15 relative error = 9.26345222751479e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.772 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.772 Order of pole (three term test) = 7.409e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.773 y[1] (closed_form) = 1.673558940235537 y[1] (numeric) = 1.673558940235535 absolute error = 1.554312234475219e-15 relative error = 9.287466351537433e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.773 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.773 Order of pole (three term test) = 3.851e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.774 y[1] (closed_form) = 1.669237292096495 y[1] (numeric) = 1.669237292096494 absolute error = 1.554312234475219e-15 relative error = 9.311511561804764e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.774 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.774 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.775 y[1] (closed_form) = 1.664932362122789 y[1] (numeric) = 1.664932362122787 absolute error = 1.554312234475219e-15 relative error = 9.335587858316785e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.775 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.775 Order of pole (three term test) = 4.161e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.776 y[1] (closed_form) = 1.660644064193857 y[1] (numeric) = 1.660644064193855 absolute error = 1.332267629550188e-15 relative error = 8.022595920920141e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.776 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.776 Order of pole (three term test) = 4.325e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.777 y[1] (closed_form) = 1.656372312742969 y[1] (numeric) = 1.656372312742967 absolute error = 1.554312234475219e-15 relative error = 9.383833710074896e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.777 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.777 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.778 y[1] (closed_form) = 1.652117022752956 y[1] (numeric) = 1.652117022752954 absolute error = 1.554312234475219e-15 relative error = 9.408003265320986e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.778 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.778 Order of pole (three term test) = 2.336e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.779 y[1] (closed_form) = 1.647878109751978 y[1] (numeric) = 1.647878109751976 absolute error = 1.77635683940025e-15 relative error = 1.077966160778487e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.779 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.779 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.78 y[1] (closed_form) = 1.643655489809336 y[1] (numeric) = 1.643655489809334 absolute error = 1.554312234475219e-15 relative error = 9.456435634547235e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.78 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.78 Order of pole (three term test) = 7.57e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.781 y[1] (closed_form) = 1.639449079531314 y[1] (numeric) = 1.639449079531313 absolute error = 1.554312234475219e-15 relative error = 9.480698448527392e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.781 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.781 Order of pole (three term test) = 5.245e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.782 y[1] (closed_form) = 1.635258796057064 y[1] (numeric) = 1.635258796057062 absolute error = 1.554312234475219e-15 relative error = 9.504992348752239e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.782 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.782 Order of pole (three term test) = 2.725e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.783 y[1] (closed_form) = 1.631084557054522 y[1] (numeric) = 1.631084557054521 absolute error = 1.554312234475219e-15 relative error = 9.529317335221777e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.783 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.783 Order of pole (three term test) = 5.663e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.784 y[1] (closed_form) = 1.626926280716368 y[1] (numeric) = 1.626926280716367 absolute error = 1.332267629550188e-15 relative error = 8.188862921088003e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.784 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.784 Order of pole (three term test) = 2.942e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.785 y[1] (closed_form) = 1.622783885756014 y[1] (numeric) = 1.622783885756013 absolute error = 1.554312234475219e-15 relative error = 9.57806056689492e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.785 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.785 Order of pole (three term test) = 6.113e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.786 y[1] (closed_form) = 1.618657291403635 y[1] (numeric) = 1.618657291403633 absolute error = 1.554312234475219e-15 relative error = 9.602478812098525e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.786 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.786 Order of pole (three term test) = 3.176e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.787 y[1] (closed_form) = 1.614546417402227 y[1] (numeric) = 1.614546417402225 absolute error = 1.554312234475219e-15 relative error = 9.626928143546821e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.787 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.787 Order of pole (three term test) = 6.598e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.788 y[1] (closed_form) = 1.61045118400371 y[1] (numeric) = 1.610451184003709 absolute error = 1.554312234475219e-15 relative error = 9.651408561239806e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.788 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.788 Order of pole (three term test) = 3.427e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.789 y[1] (closed_form) = 1.606371511965058 y[1] (numeric) = 1.606371511965057 absolute error = 1.332267629550188e-15 relative error = 8.293645770152127e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.789 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.789 Order of pole (three term test) = 3.56e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.79 y[1] (closed_form) = 1.602307322544464 y[1] (numeric) = 1.602307322544462 absolute error = 1.332267629550188e-15 relative error = 8.314682276022724e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.79 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.79 Order of pole (three term test) = 3.698e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.791 y[1] (closed_form) = 1.598258537497543 y[1] (numeric) = 1.598258537497541 absolute error = 1.554312234475219e-15 relative error = 9.725036331786896e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.791 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.791 Order of pole (three term test) = 7.682e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.792 y[1] (closed_form) = 1.594225079073564 y[1] (numeric) = 1.594225079073562 absolute error = 1.332267629550188e-15 relative error = 8.356835223821692e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.792 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.792 Order of pole (three term test) = 7.979e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.793 y[1] (closed_form) = 1.59020687001172 y[1] (numeric) = 1.590206870011718 absolute error = 1.554312234475219e-15 relative error = 9.774276943375071e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.793 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.793 Order of pole (three term test) = 8.287e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.794 y[1] (closed_form) = 1.586203833537425 y[1] (numeric) = 1.586203833537423 absolute error = 1.332267629550188e-15 relative error = 8.399094753031023e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.794 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.794 Order of pole (three term test) = 4.303e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.795 y[1] (closed_form) = 1.582215893358649 y[1] (numeric) = 1.582215893358647 absolute error = 1.332267629550188e-15 relative error = 8.420264485664575e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.795 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.795 Order of pole (three term test) = 8.937e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.796 y[1] (closed_form) = 1.578242973662281 y[1] (numeric) = 1.57824297366228 absolute error = 1.332267629550188e-15 relative error = 8.44146086365072e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.796 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.796 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.797 y[1] (closed_form) = 1.574284999110529 y[1] (numeric) = 1.574284999110527 absolute error = 1.554312234475219e-15 relative error = 9.873131201487696e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.797 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.797 Order of pole (three term test) = 4.818e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.798 y[1] (closed_form) = 1.570341894837344 y[1] (numeric) = 1.570341894837342 absolute error = 1.554312234475219e-15 relative error = 9.897922481627576e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.798 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.798 Order of pole (three term test) = 5.003e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.799 y[1] (closed_form) = 1.566413586444883 y[1] (numeric) = 1.566413586444882 absolute error = 1.77635683940025e-15 relative error = 1.134027982629959e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.799 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.799 Order of pole (three term test) = 5.195e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8 y[1] (closed_form) = 1.5625 y[1] (numeric) = 1.562499999999998 absolute error = 1.77635683940025e-15 relative error = 1.13686837721616e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8 Order of pole (three term test) = 5.393e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.801 y[1] (closed_form) = 1.558601062030764 y[1] (numeric) = 1.558601062030762 absolute error = 1.554312234475219e-15 relative error = 9.972482839515352e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.801 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.801 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.802 y[1] (closed_form) = 1.554716699523013 y[1] (numeric) = 1.554716699523011 absolute error = 1.332267629550188e-15 relative error = 8.569198683971992e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.802 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.802 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.803 y[1] (closed_form) = 1.550846839916936 y[1] (numeric) = 1.550846839916935 absolute error = 1.332267629550188e-15 relative error = 8.590581579426272e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.803 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.803 Order of pole (three term test) = 6.034e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.804 y[1] (closed_form) = 1.546991411103685 y[1] (numeric) = 1.546991411103684 absolute error = 1.332267629550188e-15 relative error = 8.611991120233144e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.804 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.804 Order of pole (three term test) = 6.264e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.805 y[1] (closed_form) = 1.543150341422013 y[1] (numeric) = 1.543150341422012 absolute error = 1.332267629550188e-15 relative error = 8.633427306392606e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.805 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.805 Order of pole (three term test) = 3.251e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.806 y[1] (closed_form) = 1.539323559654945 y[1] (numeric) = 1.539323559654944 absolute error = 1.332267629550188e-15 relative error = 8.654890137904659e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.806 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.806 Order of pole (three term test) = 3.374e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8070000000000001 y[1] (closed_form) = 1.53551099502648 y[1] (numeric) = 1.535510995026478 absolute error = 1.332267629550188e-15 relative error = 8.676379614769305e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.807 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.807 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8080000000000001 y[1] (closed_form) = 1.531712577198314 y[1] (numeric) = 1.531712577198312 absolute error = 1.554312234475219e-15 relative error = 1.01475450264843e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.808 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.808 Order of pole (three term test) = 3.635e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8090000000000001 y[1] (closed_form) = 1.527928236266599 y[1] (numeric) = 1.527928236266597 absolute error = 1.332267629550188e-15 relative error = 8.719438504556366e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.809 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.809 Order of pole (three term test) = 7.544e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8100000000000001 y[1] (closed_form) = 1.524157902758726 y[1] (numeric) = 1.524157902758724 absolute error = 1.332267629550188e-15 relative error = 8.741007917478784e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.81 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.81 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8110000000000001 y[1] (closed_form) = 1.520401507630135 y[1] (numeric) = 1.520401507630133 absolute error = 1.332267629550188e-15 relative error = 8.762603975753793e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.811 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.811 Order of pole (three term test) = 4.062e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8120000000000001 y[1] (closed_form) = 1.516658982261156 y[1] (numeric) = 1.516658982261155 absolute error = 1.332267629550188e-15 relative error = 8.784226679381392e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.812 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.812 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8130000000000001 y[1] (closed_form) = 1.512930258453876 y[1] (numeric) = 1.512930258453874 absolute error = 1.554312234475219e-15 relative error = 1.027352203308851e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.813 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.813 Order of pole (three term test) = 8.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8140000000000001 y[1] (closed_form) = 1.509215268429027 y[1] (numeric) = 1.509215268429026 absolute error = 1.332267629550188e-15 relative error = 8.827552022694363e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.814 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.814 Order of pole (three term test) = 9.076e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8150000000000001 y[1] (closed_form) = 1.505513944822914 y[1] (numeric) = 1.505513944822912 absolute error = 1.332267629550188e-15 relative error = 8.849254662379736e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.815 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.815 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8160000000000001 y[1] (closed_form) = 1.501826220684352 y[1] (numeric) = 1.501826220684351 absolute error = 1.332267629550188e-15 relative error = 8.8709839474177e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.816 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.816 Order of pole (three term test) = 2.442e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8170000000000001 y[1] (closed_form) = 1.498152029471647 y[1] (numeric) = 1.498152029471645 absolute error = 1.332267629550188e-15 relative error = 8.892739877808254e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.817 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.817 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8180000000000001 y[1] (closed_form) = 1.494491305049587 y[1] (numeric) = 1.494491305049586 absolute error = 1.110223024625157e-15 relative error = 7.428768711292834e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.818 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.818 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8190000000000001 y[1] (closed_form) = 1.490843981686472 y[1] (numeric) = 1.490843981686471 absolute error = 1.110223024625157e-15 relative error = 7.446943062205947e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.819 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.819 Order of pole (three term test) = 2.727e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8200000000000001 y[1] (closed_form) = 1.48720999405116 y[1] (numeric) = 1.487209994051159 absolute error = 1.110223024625157e-15 relative error = 7.465139617579554e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.82 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.82 Order of pole (three term test) = 2.828e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8210000000000001 y[1] (closed_form) = 1.48358927721014 y[1] (numeric) = 1.483589277210139 absolute error = 1.110223024625157e-15 relative error = 7.483358377413653e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.821 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.821 Order of pole (three term test) = 2.934e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8220000000000001 y[1] (closed_form) = 1.479981766624635 y[1] (numeric) = 1.479981766624634 absolute error = 1.110223024625157e-15 relative error = 7.501599341708245e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.822 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.822 Order of pole (three term test) = 3.043e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8230000000000001 y[1] (closed_form) = 1.476387398147724 y[1] (numeric) = 1.476387398147723 absolute error = 1.110223024625157e-15 relative error = 7.519862510463329e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.823 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.823 Order of pole (three term test) = 3.156e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8240000000000001 y[1] (closed_form) = 1.472806108021491 y[1] (numeric) = 1.47280610802149 absolute error = 1.110223024625157e-15 relative error = 7.538147883678904e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.824 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.824 Order of pole (three term test) = 6.545e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8250000000000001 y[1] (closed_form) = 1.469237832874196 y[1] (numeric) = 1.469237832874195 absolute error = 1.110223024625157e-15 relative error = 7.556455461354973e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.825 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.825 Order of pole (three term test) = 3.394e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8260000000000001 y[1] (closed_form) = 1.465682509717475 y[1] (numeric) = 1.465682509717473 absolute error = 1.332267629550188e-15 relative error = 9.089742292189842e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.826 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.826 Order of pole (three term test) = 7.039e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8270000000000001 y[1] (closed_form) = 1.462140075943555 y[1] (numeric) = 1.462140075943554 absolute error = 1.332267629550188e-15 relative error = 9.111764676106306e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.827 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.827 Order of pole (three term test) = 3.65e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8280000000000001 y[1] (closed_form) = 1.458610469322504 y[1] (numeric) = 1.458610469322503 absolute error = 1.110223024625157e-15 relative error = 7.611511421146135e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.828 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.828 Order of pole (three term test) = 3.784e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8290000000000001 y[1] (closed_form) = 1.455093627999493 y[1] (numeric) = 1.455093627999492 absolute error = 1.110223024625157e-15 relative error = 7.629907816664174e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.829 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.829 Order of pole (three term test) = 3.924e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8300000000000001 y[1] (closed_form) = 1.451589490492089 y[1] (numeric) = 1.451589490492087 absolute error = 1.110223024625157e-15 relative error = 7.648326416642706e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.83 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.83 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8310000000000001 y[1] (closed_form) = 1.448097995687564 y[1] (numeric) = 1.448097995687563 absolute error = 1.110223024625157e-15 relative error = 7.666767221081729e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.831 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.831 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8320000000000001 y[1] (closed_form) = 1.444619082840237 y[1] (numeric) = 1.444619082840235 absolute error = 1.332267629550188e-15 relative error = 9.222276275977493e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.832 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.832 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8330000000000001 y[1] (closed_form) = 1.441152691568824 y[1] (numeric) = 1.441152691568823 absolute error = 1.332267629550188e-15 relative error = 9.244458532009504e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.833 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.833 Order of pole (three term test) = 9.067e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8340000000000001 y[1] (closed_form) = 1.437698761853826 y[1] (numeric) = 1.437698761853825 absolute error = 1.110223024625157e-15 relative error = 7.722222861161756e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.834 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.834 Order of pole (three term test) = 2.35e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8350000000000001 y[1] (closed_form) = 1.434257234034924 y[1] (numeric) = 1.434257234034923 absolute error = 1.332267629550188e-15 relative error = 9.288902980131298e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.835 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.835 Order of pole (three term test) = 2.436e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8360000000000001 y[1] (closed_form) = 1.430828048808406 y[1] (numeric) = 1.430828048808405 absolute error = 1.110223024625157e-15 relative error = 7.759304310184236e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.836 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.836 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8370000000000001 y[1] (closed_form) = 1.427411147224613 y[1] (numeric) = 1.427411147224612 absolute error = 1.332267629550188e-15 relative error = 9.333454009663457e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.837 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.837 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8380000000000001 y[1] (closed_form) = 1.424006470685403 y[1] (numeric) = 1.424006470685401 absolute error = 1.332267629550188e-15 relative error = 9.355769492458423e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.838 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.838 Order of pole (three term test) = 5.425e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8390000000000001 y[1] (closed_form) = 1.420613960941639 y[1] (numeric) = 1.420613960941638 absolute error = 1.332267629550188e-15 relative error = 9.378111620605979e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.839 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.839 Order of pole (three term test) = 2.811e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8400000000000001 y[1] (closed_form) = 1.417233560090703 y[1] (numeric) = 1.417233560090701 absolute error = 1.554312234475219e-15 relative error = 1.096722712645715e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.84 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.84 Order of pole (three term test) = 5.827e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8410000000000001 y[1] (closed_form) = 1.413865210574015 y[1] (numeric) = 1.413865210574013 absolute error = 1.332267629550188e-15 relative error = 9.422875812958866e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.841 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.841 Order of pole (three term test) = 3.02e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8420000000000001 y[1] (closed_form) = 1.410508855174593 y[1] (numeric) = 1.410508855174591 absolute error = 1.332267629550188e-15 relative error = 9.445297877164195e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.842 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.842 Order of pole (three term test) = 6.258e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8430000000000001 y[1] (closed_form) = 1.407164437014616 y[1] (numeric) = 1.407164437014615 absolute error = 1.554312234475219e-15 relative error = 1.10457043511758e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.843 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.843 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8440000000000001 y[1] (closed_form) = 1.403831899553019 y[1] (numeric) = 1.403831899553018 absolute error = 1.110223024625157e-15 relative error = 7.908518284693858e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.844 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.844 Order of pole (three term test) = 3.36e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8450000000000001 y[1] (closed_form) = 1.400511186583103 y[1] (numeric) = 1.400511186583101 absolute error = 1.332267629550188e-15 relative error = 9.512723941895731e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.845 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.845 Order of pole (three term test) = 6.963e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8460000000000001 y[1] (closed_form) = 1.397202242230158 y[1] (numeric) = 1.397202242230157 absolute error = 1.554312234475219e-15 relative error = 1.112446135209666e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.846 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.846 Order of pole (three term test) = 3.607e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8470000000000001 y[1] (closed_form) = 1.393905010949124 y[1] (numeric) = 1.393905010949122 absolute error = 1.554312234475219e-15 relative error = 1.115077585822633e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.847 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.847 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8480000000000001 y[1] (closed_form) = 1.39061943752225 y[1] (numeric) = 1.390619437522248 absolute error = 1.332267629550188e-15 relative error = 9.580389814800585e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.848 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.848 Order of pole (three term test) = 7.744e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8490000000000001 y[1] (closed_form) = 1.387345467056788 y[1] (numeric) = 1.387345467056787 absolute error = 1.332267629550188e-15 relative error = 9.602998396474052e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.849 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.849 Order of pole (three term test) = 4.011e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8500000000000001 y[1] (closed_form) = 1.384083044982699 y[1] (numeric) = 1.384083044982697 absolute error = 1.332267629550188e-15 relative error = 9.62563362350011e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.85 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.85 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8510000000000001 y[1] (closed_form) = 1.380832117050377 y[1] (numeric) = 1.380832117050375 absolute error = 1.554312234475219e-15 relative error = 1.125634474519188e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.851 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.851 Order of pole (three term test) = 4.305e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8520000000000001 y[1] (closed_form) = 1.377592629328396 y[1] (numeric) = 1.377592629328394 absolute error = 1.332267629550188e-15 relative error = 9.670984013609998e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.852 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.852 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8530000000000001 y[1] (closed_form) = 1.374364528201273 y[1] (numeric) = 1.374364528201271 absolute error = 1.332267629550188e-15 relative error = 9.693699176693828e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.853 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.853 Order of pole (three term test) = 4.619e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8540000000000001 y[1] (closed_form) = 1.371147760367248 y[1] (numeric) = 1.371147760367247 absolute error = 1.332267629550188e-15 relative error = 9.71644098513025e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.854 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.854 Order of pole (three term test) = 9.568e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8550000000000001 y[1] (closed_form) = 1.367942272836086 y[1] (numeric) = 1.367942272836085 absolute error = 1.554312234475219e-15 relative error = 1.136241101207247e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.855 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.855 Order of pole (three term test) = 2.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8560000000000001 y[1] (closed_form) = 1.364748012926893 y[1] (numeric) = 1.364748012926891 absolute error = 1.332267629550188e-15 relative error = 9.762004538060868e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.856 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.856 Order of pole (three term test) = 2.566e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8570000000000001 y[1] (closed_form) = 1.361564928265951 y[1] (numeric) = 1.36156492826595 absolute error = 1.554312234475219e-15 relative error = 1.14156306629809e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.857 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.857 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8580000000000001 y[1] (closed_form) = 1.358392966784575 y[1] (numeric) = 1.358392966784573 absolute error = 1.554312234475219e-15 relative error = 1.144228711780215e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.858 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.858 Order of pole (three term test) = 2.752e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8590000000000001 y[1] (closed_form) = 1.355232076716977 y[1] (numeric) = 1.355232076716976 absolute error = 1.554312234475219e-15 relative error = 1.146897465886809e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.859 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.859 Order of pole (three term test) = 5.7e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8600000000000001 y[1] (closed_form) = 1.352082206598161 y[1] (numeric) = 1.352082206598159 absolute error = 1.332267629550188e-15 relative error = 9.853451388153192e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.86 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.86 Order of pole (three term test) = 2.951e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8610000000000001 y[1] (closed_form) = 1.348943305261823 y[1] (numeric) = 1.348943305261821 absolute error = 1.332267629550188e-15 relative error = 9.876379714057752e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.861 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.861 Order of pole (three term test) = 3.056e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8620000000000001 y[1] (closed_form) = 1.345815321838276 y[1] (numeric) = 1.345815321838274 absolute error = 1.332267629550188e-15 relative error = 9.899334685314901e-14 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 16 h = -0.001 Radius of convergence (given) for eq 1 = 0.862 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.862 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8630000000000001 y[1] (closed_form) = 1.342698205752387 y[1] (numeric) = 1.342698205752386 absolute error = 1.554312234475219e-15 relative error = 1.157603568557875e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.863 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.863 Order of pole (three term test) = 6.552e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8640000000000001 y[1] (closed_form) = 1.339591906721536 y[1] (numeric) = 1.339591906721534 absolute error = 1.554312234475219e-15 relative error = 1.160287865786813e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.864 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.864 Order of pole (three term test) = 6.784e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8650000000000001 y[1] (closed_form) = 1.336496374753583 y[1] (numeric) = 1.336496374753582 absolute error = 1.554312234475219e-15 relative error = 1.162975271640221e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.865 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.865 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8660000000000001 y[1] (closed_form) = 1.333411560144862 y[1] (numeric) = 1.33341156014486 absolute error = 1.554312234475219e-15 relative error = 1.165665786118098e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.866 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.866 Order of pole (three term test) = 7.271e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8670000000000001 y[1] (closed_form) = 1.33033741347818 y[1] (numeric) = 1.330337413478179 absolute error = 1.332267629550188e-15 relative error = 1.001450922188952e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.867 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.867 Order of pole (three term test) = 7.527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8680000000000001 y[1] (closed_form) = 1.327273885620845 y[1] (numeric) = 1.327273885620844 absolute error = 1.332267629550188e-15 relative error = 1.003762406526221e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.868 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.868 Order of pole (three term test) = 7.792e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8690000000000001 y[1] (closed_form) = 1.324220927722697 y[1] (numeric) = 1.324220927722696 absolute error = 1.332267629550188e-15 relative error = 1.00607655539875e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.869 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.869 Order of pole (three term test) = 4.033e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8700000000000001 y[1] (closed_form) = 1.321178491214163 y[1] (numeric) = 1.321178491214161 absolute error = 1.554312234475219e-15 relative error = 1.176458930274293e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.87 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.87 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8710000000000001 y[1] (closed_form) = 1.318146527804323 y[1] (numeric) = 1.318146527804322 absolute error = 1.332267629550188e-15 relative error = 1.010712846749584e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.871 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.871 Order of pole (three term test) = 4.321e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8720000000000001 y[1] (closed_form) = 1.315124989479 y[1] (numeric) = 1.315124989478998 absolute error = 1.332267629550188e-15 relative error = 1.01303498922789e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.872 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.872 Order of pole (three term test) = 4.472e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8730000000000001 y[1] (closed_form) = 1.31211382849885 y[1] (numeric) = 1.312113828498848 absolute error = 1.554312234475219e-15 relative error = 1.184586428948365e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.873 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.873 Order of pole (three term test) = 4.629e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8740000000000001 y[1] (closed_form) = 1.309112997397483 y[1] (numeric) = 1.309112997397482 absolute error = 1.554312234475219e-15 relative error = 1.187301812421993e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.874 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.874 Order of pole (three term test) = 2.395e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8750000000000001 y[1] (closed_form) = 1.306122448979592 y[1] (numeric) = 1.30612244897959 absolute error = 1.554312234475219e-15 relative error = 1.19002030452009e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.875 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.875 Order of pole (three term test) = 2.479e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8760000000000001 y[1] (closed_form) = 1.303142136319092 y[1] (numeric) = 1.303142136319091 absolute error = 1.554312234475219e-15 relative error = 1.192741905242656e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.876 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.876 Order of pole (three term test) = 2.565e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8770000000000001 y[1] (closed_form) = 1.300172012757287 y[1] (numeric) = 1.300172012757286 absolute error = 1.332267629550188e-15 relative error = 1.024685669648307e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.877 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.877 Order of pole (three term test) = 5.309e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8780000000000001 y[1] (closed_form) = 1.297212031901038 y[1] (numeric) = 1.297212031901037 absolute error = 1.332267629550188e-15 relative error = 1.027023799338167e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.878 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.878 Order of pole (three term test) = 2.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8790000000000001 y[1] (closed_form) = 1.294262147620951 y[1] (numeric) = 1.29426214762095 absolute error = 1.332267629550188e-15 relative error = 1.029364593563287e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.879 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.879 Order of pole (three term test) = 8.527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8800000000000001 y[1] (closed_form) = 1.291322314049586 y[1] (numeric) = 1.291322314049585 absolute error = 1.554312234475219e-15 relative error = 1.20365939437761e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.88 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.88 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8810000000000001 y[1] (closed_form) = 1.288392485579667 y[1] (numeric) = 1.288392485579665 absolute error = 1.554312234475219e-15 relative error = 1.206396538222521e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.881 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.881 Order of pole (three term test) = 6.086e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8820000000000001 y[1] (closed_form) = 1.285472616862315 y[1] (numeric) = 1.285472616862314 absolute error = 1.554312234475219e-15 relative error = 1.209136790691901e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.882 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.882 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8830000000000001 y[1] (closed_form) = 1.282562662805298 y[1] (numeric) = 1.282562662805296 absolute error = 1.77635683940025e-15 relative error = 1.385005887755142e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.883 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.883 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8840000000000001 y[1] (closed_form) = 1.279662578571282 y[1] (numeric) = 1.27966257857128 absolute error = 1.554312234475219e-15 relative error = 1.214626621504067e-13 % Desired digits = 8 Estimated correct digits = 13 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.884 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.884 Order of pole (three term test) = 6.739e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8850000000000001 y[1] (closed_form) = 1.276772319576111 y[1] (numeric) = 1.27677231957611 absolute error = 1.554312234475219e-15 relative error = 1.217376199846854e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.885 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.885 Order of pole (three term test) = 3.486e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8860000000000001 y[1] (closed_form) = 1.27389184148709 y[1] (numeric) = 1.273891841487088 absolute error = 1.77635683940025e-15 relative error = 1.394433013501839e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.886 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.886 Order of pole (three term test) = 7.212e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8870000000000001 y[1] (closed_form) = 1.271021100221285 y[1] (numeric) = 1.271021100221283 absolute error = 1.77635683940025e-15 relative error = 1.397582494178096e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.887 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.887 Order of pole (three term test) = 3.73e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8880000000000001 y[1] (closed_form) = 1.268160051943835 y[1] (numeric) = 1.268160051943834 absolute error = 1.77635683940025e-15 relative error = 1.400735527568032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.888 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.888 Order of pole (three term test) = 3.858e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8890000000000001 y[1] (closed_form) = 1.265308653066285 y[1] (numeric) = 1.265308653066284 absolute error = 1.77635683940025e-15 relative error = 1.403892113671646e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.889 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.889 Order of pole (three term test) = 7.982e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8900000000000001 y[1] (closed_form) = 1.262466860244918 y[1] (numeric) = 1.262466860244917 absolute error = 1.77635683940025e-15 relative error = 1.407052252488939e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.89 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.89 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8910000000000001 y[1] (closed_form) = 1.259634630379112 y[1] (numeric) = 1.25963463037911 absolute error = 1.554312234475219e-15 relative error = 1.233938951017422e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.891 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.891 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8920000000000001 y[1] (closed_form) = 1.256811920609704 y[1] (numeric) = 1.256811920609703 absolute error = 1.77635683940025e-15 relative error = 1.413383188264561e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.892 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.892 Order of pole (three term test) = 8.83e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8930000000000001 y[1] (closed_form) = 1.253998688317371 y[1] (numeric) = 1.25399868831737 absolute error = 1.554312234475219e-15 relative error = 1.23948473707003e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.893 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.893 Order of pole (three term test) = 4.566e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8940000000000001 y[1] (closed_form) = 1.25119489112102 y[1] (numeric) = 1.251194891121018 absolute error = 1.77635683940025e-15 relative error = 1.419728334894899e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.894 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.894 Order of pole (three term test) = 2.361e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8950000000000001 y[1] (closed_form) = 1.24840048687619 y[1] (numeric) = 1.248400486876188 absolute error = 1.77635683940025e-15 relative error = 1.422906237280586e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.895 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.895 Order of pole (three term test) = 2.442e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8960000000000001 y[1] (closed_form) = 1.245615433673469 y[1] (numeric) = 1.245615433673467 absolute error = 1.77635683940025e-15 relative error = 1.426087692379952e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.896 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.896 Order of pole (three term test) = 2.525e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8970000000000001 y[1] (closed_form) = 1.242839689836926 y[1] (numeric) = 1.242839689836925 absolute error = 1.554312234475219e-15 relative error = 1.250613612668872e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.897 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.897 Order of pole (three term test) = 2.611e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8980000000000001 y[1] (closed_form) = 1.240073213922549 y[1] (numeric) = 1.240073213922548 absolute error = 1.554312234475219e-15 relative error = 1.253403603129755e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.898 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.898 Order of pole (three term test) = 5.399e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8990000000000001 y[1] (closed_form) = 1.237315964716698 y[1] (numeric) = 1.237315964716696 absolute error = 1.77635683940025e-15 relative error = 1.435653373960122e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.899 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.899 Order of pole (three term test) = 5.582e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000001 y[1] (closed_form) = 1.234567901234568 y[1] (numeric) = 1.234567901234566 absolute error = 1.77635683940025e-15 relative error = 1.438849039914203e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9 Order of pole (three term test) = 2.886e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9010000000000001 y[1] (closed_form) = 1.231828982718671 y[1] (numeric) = 1.231828982718669 absolute error = 1.998401444325282e-15 relative error = 1.622304290904708e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.901 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.901 Order of pole (three term test) = 5.967e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9020000000000001 y[1] (closed_form) = 1.229099168637322 y[1] (numeric) = 1.22909916863732 absolute error = 1.77635683940025e-15 relative error = 1.445251029963402e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.902 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.902 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9030000000000001 y[1] (closed_form) = 1.226378418683139 y[1] (numeric) = 1.226378418683137 absolute error = 1.998401444325282e-15 relative error = 1.629514523315834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.903 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.903 Order of pole (three term test) = 3.189e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9040000000000001 y[1] (closed_form) = 1.223666692771556 y[1] (numeric) = 1.223666692771554 absolute error = 1.998401444325282e-15 relative error = 1.63312563472573e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.904 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.904 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9050000000000001 y[1] (closed_form) = 1.220963951039345 y[1] (numeric) = 1.220963951039343 absolute error = 1.998401444325282e-15 relative error = 1.636740742938514e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.905 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.905 Order of pole (three term test) = 3.407e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9060000000000001 y[1] (closed_form) = 1.218270153843155 y[1] (numeric) = 1.218270153843153 absolute error = 1.77635683940025e-15 relative error = 1.458097642625945e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.906 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.906 Order of pole (three term test) = 3.522e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9070000000000001 y[1] (closed_form) = 1.215585261758052 y[1] (numeric) = 1.21558526175805 absolute error = 1.77635683940025e-15 relative error = 1.461318177575777e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.907 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.907 Order of pole (three term test) = 3.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9080000000000001 y[1] (closed_form) = 1.212909235576083 y[1] (numeric) = 1.212909235576081 absolute error = 1.77635683940025e-15 relative error = 1.464542265239289e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.908 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.908 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9090000000000001 y[1] (closed_form) = 1.21024203630484 y[1] (numeric) = 1.210242036304839 absolute error = 1.77635683940025e-15 relative error = 1.467769905616479e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.909 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.909 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9100000000000001 y[1] (closed_form) = 1.207583625166042 y[1] (numeric) = 1.207583625166041 absolute error = 1.77635683940025e-15 relative error = 1.471001098707348e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.91 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.91 Order of pole (three term test) = 4.02e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9110000000000001 y[1] (closed_form) = 1.204933963594125 y[1] (numeric) = 1.204933963594123 absolute error = 1.998401444325282e-15 relative error = 1.658515325075882e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.911 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.911 Order of pole (three term test) = 8.309e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9120000000000001 y[1] (closed_form) = 1.202293013234841 y[1] (numeric) = 1.202293013234839 absolute error = 1.77635683940025e-15 relative error = 1.477474143030123e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.912 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.912 Order of pole (three term test) = 4.294e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9130000000000001 y[1] (closed_form) = 1.199660735943875 y[1] (numeric) = 1.199660735943873 absolute error = 1.77635683940025e-15 relative error = 1.480715994262028e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.913 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.913 Order of pole (three term test) = 4.437e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9140000000000001 y[1] (closed_form) = 1.197037093785462 y[1] (numeric) = 1.19703709378546 absolute error = 1.998401444325282e-15 relative error = 1.669456572983563e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.914 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.914 Order of pole (three term test) = 4.585e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9150000000000001 y[1] (closed_form) = 1.194422049031025 y[1] (numeric) = 1.194422049031023 absolute error = 1.998401444325282e-15 relative error = 1.673111649225234e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.915 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.915 Order of pole (three term test) = 4.738e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9160000000000001 y[1] (closed_form) = 1.191815564157815 y[1] (numeric) = 1.191815564157813 absolute error = 1.998401444325282e-15 relative error = 1.676770722269794e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.916 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.916 Order of pole (three term test) = 2.448e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9170000000000001 y[1] (closed_form) = 1.189217601847568 y[1] (numeric) = 1.189217601847566 absolute error = 1.77635683940025e-15 relative error = 1.493718926326438e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.917 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.917 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9180000000000001 y[1] (closed_form) = 1.186628124985167 y[1] (numeric) = 1.186628124985165 absolute error = 1.77635683940025e-15 relative error = 1.496978541126737e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.918 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.918 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9190000000000002 y[1] (closed_form) = 1.184047096657316 y[1] (numeric) = 1.184047096657314 absolute error = 1.77635683940025e-15 relative error = 1.500241708640716e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.919 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.919 Order of pole (three term test) = 5.401e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9200000000000002 y[1] (closed_form) = 1.181474480151228 y[1] (numeric) = 1.181474480151226 absolute error = 1.77635683940025e-15 relative error = 1.503508428868373e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.92 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.92 Order of pole (three term test) = 5.58e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9210000000000002 y[1] (closed_form) = 1.178910238953316 y[1] (numeric) = 1.178910238953314 absolute error = 1.77635683940025e-15 relative error = 1.506778701809708e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.921 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.921 Order of pole (three term test) = 2.882e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9220000000000002 y[1] (closed_form) = 1.176354336747897 y[1] (numeric) = 1.176354336747896 absolute error = 1.77635683940025e-15 relative error = 1.510052527464723e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.922 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.922 Order of pole (three term test) = 5.955e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9230000000000002 y[1] (closed_form) = 1.173806737415911 y[1] (numeric) = 1.173806737415909 absolute error = 1.554312234475219e-15 relative error = 1.32416366760424e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.923 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.923 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9240000000000002 y[1] (closed_form) = 1.171267405033638 y[1] (numeric) = 1.171267405033637 absolute error = 1.554312234475219e-15 relative error = 1.327034482301315e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.924 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.924 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9250000000000002 y[1] (closed_form) = 1.168736303871439 y[1] (numeric) = 1.168736303871437 absolute error = 1.77635683940025e-15 relative error = 1.51989532071184e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.925 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.925 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9260000000000002 y[1] (closed_form) = 1.166213398392491 y[1] (numeric) = 1.166213398392489 absolute error = 1.77635683940025e-15 relative error = 1.52318335722157e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.926 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.926 Order of pole (three term test) = 6.781e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9270000000000002 y[1] (closed_form) = 1.163698653251548 y[1] (numeric) = 1.163698653251547 absolute error = 1.554312234475219e-15 relative error = 1.335665578139356e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.927 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.927 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9280000000000002 y[1] (closed_form) = 1.161192033293698 y[1] (numeric) = 1.161192033293696 absolute error = 1.554312234475219e-15 relative error = 1.338548827334308e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.928 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.928 Order of pole (three term test) = 3.617e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9290000000000002 y[1] (closed_form) = 1.158693503553133 y[1] (numeric) = 1.158693503553132 absolute error = 1.554312234475219e-15 relative error = 1.341435185153728e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.929 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.929 Order of pole (three term test) = 3.736e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9300000000000002 y[1] (closed_form) = 1.156203029251936 y[1] (numeric) = 1.156203029251935 absolute error = 1.554312234475219e-15 relative error = 1.344324651597618e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.93 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.93 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9310000000000002 y[1] (closed_form) = 1.153720575798865 y[1] (numeric) = 1.153720575798863 absolute error = 1.77635683940025e-15 relative error = 1.539676830475401e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.931 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.931 Order of pole (three term test) = 1.196e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9320000000000002 y[1] (closed_form) = 1.151246108788152 y[1] (numeric) = 1.15124610878815 absolute error = 1.77635683940025e-15 relative error = 1.542986183267204e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.932 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.932 Order of pole (three term test) = 4.115e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9330000000000002 y[1] (closed_form) = 1.148779593998315 y[1] (numeric) = 1.148779593998314 absolute error = 1.554312234475219e-15 relative error = 1.3530117026761e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.933 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.933 Order of pole (three term test) = 4.25e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9340000000000002 y[1] (closed_form) = 1.146320997390973 y[1] (numeric) = 1.146320997390971 absolute error = 1.77635683940025e-15 relative error = 1.549615546991845e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.934 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.934 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9350000000000002 y[1] (closed_form) = 1.143870285109668 y[1] (numeric) = 1.143870285109666 absolute error = 1.77635683940025e-15 relative error = 1.552935557924684e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.935 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.935 Order of pole (three term test) = 4.532e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9360000000000002 y[1] (closed_form) = 1.141427423478705 y[1] (numeric) = 1.141427423478703 absolute error = 1.554312234475219e-15 relative error = 1.361726731374802e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.936 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.936 Order of pole (three term test) = 2.34e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9370000000000002 y[1] (closed_form) = 1.138992379001992 y[1] (numeric) = 1.13899237900199 absolute error = 1.77635683940025e-15 relative error = 1.559586237931399e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.937 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.937 Order of pole (three term test) = 4.832e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9380000000000002 y[1] (closed_form) = 1.136565118361891 y[1] (numeric) = 1.136565118361889 absolute error = 1.554312234475219e-15 relative error = 1.367552293629615e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.938 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.938 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9390000000000002 y[1] (closed_form) = 1.134145608418082 y[1] (numeric) = 1.13414560841808 absolute error = 1.554312234475219e-15 relative error = 1.370469737693725e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.939 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.939 Order of pole (three term test) = 7.727e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9400000000000002 y[1] (closed_form) = 1.131733816206428 y[1] (numeric) = 1.131733816206426 absolute error = 1.77635683940025e-15 relative error = 1.569588903294062e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.94 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.94 Order of pole (three term test) = 2.659e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9410000000000002 y[1] (closed_form) = 1.129329708937854 y[1] (numeric) = 1.129329708937852 absolute error = 1.77635683940025e-15 relative error = 1.572930230508974e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.941 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.941 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9420000000000002 y[1] (closed_form) = 1.126933253997232 y[1] (numeric) = 1.12693325399723 absolute error = 1.77635683940025e-15 relative error = 1.576275110437564e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.942 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.942 Order of pole (three term test) = 5.669e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9430000000000002 y[1] (closed_form) = 1.124544418942276 y[1] (numeric) = 1.124544418942274 absolute error = 1.77635683940025e-15 relative error = 1.579623543079834e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.943 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.943 Order of pole (three term test) = 2.926e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9440000000000002 y[1] (closed_form) = 1.122163171502441 y[1] (numeric) = 1.12216317150244 absolute error = 1.77635683940025e-15 relative error = 1.582975528435782e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.944 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.944 Order of pole (three term test) = 3.02e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9450000000000002 y[1] (closed_form) = 1.119789479577839 y[1] (numeric) = 1.119789479577837 absolute error = 1.77635683940025e-15 relative error = 1.586331066505409e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.945 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.945 Order of pole (three term test) = 3.118e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9460000000000002 y[1] (closed_form) = 1.117423311238149 y[1] (numeric) = 1.117423311238148 absolute error = 1.77635683940025e-15 relative error = 1.589690157288715e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.946 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.946 Order of pole (three term test) = 6.437e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9470000000000002 y[1] (closed_form) = 1.115064634721551 y[1] (numeric) = 1.115064634721549 absolute error = 1.77635683940025e-15 relative error = 1.5930528007857e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.947 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.947 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9480000000000002 y[1] (closed_form) = 1.112713418433655 y[1] (numeric) = 1.112713418433653 absolute error = 1.77635683940025e-15 relative error = 1.596418996996363e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.948 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.948 Order of pole (three term test) = 6.858e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9490000000000002 y[1] (closed_form) = 1.110369630946445 y[1] (numeric) = 1.110369630946443 absolute error = 1.77635683940025e-15 relative error = 1.599788745920706e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.949 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.949 Order of pole (three term test) = 3.539e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9500000000000002 y[1] (closed_form) = 1.108033240997229 y[1] (numeric) = 1.108033240997228 absolute error = 1.77635683940025e-15 relative error = 1.603162047558727e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.95 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.95 Order of pole (three term test) = 3.653e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9510000000000002 y[1] (closed_form) = 1.105704217487596 y[1] (numeric) = 1.105704217487594 absolute error = 1.998401444325282e-15 relative error = 1.80735626464923e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.951 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.951 Order of pole (three term test) = 3.77e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9520000000000002 y[1] (closed_form) = 1.103382529482381 y[1] (numeric) = 1.103382529482379 absolute error = 1.77635683940025e-15 relative error = 1.609919308975805e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.952 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.952 Order of pole (three term test) = 7.781e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9530000000000002 y[1] (closed_form) = 1.101068146208637 y[1] (numeric) = 1.101068146208635 absolute error = 1.998401444325282e-15 relative error = 1.81496617734922e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.953 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.953 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9540000000000002 y[1] (closed_form) = 1.098761037054617 y[1] (numeric) = 1.098761037054615 absolute error = 1.998401444325282e-15 relative error = 1.818777128903549e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.954 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.954 Order of pole (three term test) = 8.287e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9550000000000002 y[1] (closed_form) = 1.096461171568761 y[1] (numeric) = 1.096461171568759 absolute error = 1.998401444325282e-15 relative error = 1.822592077260766e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.955 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.955 Order of pole (three term test) = 8.552e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9560000000000002 y[1] (closed_form) = 1.094168519458693 y[1] (numeric) = 1.094168519458691 absolute error = 1.998401444325282e-15 relative error = 1.826411022420871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.956 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.956 Order of pole (three term test) = 8.824e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9570000000000002 y[1] (closed_form) = 1.091883050590217 y[1] (numeric) = 1.091883050590215 absolute error = 1.77635683940025e-15 relative error = 1.626874635007881e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.957 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.957 Order of pole (three term test) = 4.553e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9580000000000002 y[1] (closed_form) = 1.089604734986336 y[1] (numeric) = 1.089604734986334 absolute error = 1.998401444325282e-15 relative error = 1.834060903149749e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.958 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.958 Order of pole (three term test) = 7.046e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9590000000000002 y[1] (closed_form) = 1.087333542826262 y[1] (numeric) = 1.08733354282626 absolute error = 1.998401444325282e-15 relative error = 1.83789183871852e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.959 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.959 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9600000000000002 y[1] (closed_form) = 1.085069444444444 y[1] (numeric) = 1.085069444444442 absolute error = 1.77635683940025e-15 relative error = 1.637090463191272e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.96 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.96 Order of pole (three term test) = 7.501e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9610000000000002 y[1] (closed_form) = 1.082812410329597 y[1] (numeric) = 1.082812410329595 absolute error = 1.77635683940025e-15 relative error = 1.640502844679759e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.961 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.961 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9620000000000002 y[1] (closed_form) = 1.080562411123741 y[1] (numeric) = 1.08056241112374 absolute error = 1.77635683940025e-15 relative error = 1.643918778881926e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.962 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.962 Order of pole (three term test) = 2.662e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9630000000000002 y[1] (closed_form) = 1.078319417621248 y[1] (numeric) = 1.078319417621247 absolute error = 1.77635683940025e-15 relative error = 1.647338265797771e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.963 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.963 Order of pole (three term test) = 8.237e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9640000000000002 y[1] (closed_form) = 1.076083400767893 y[1] (numeric) = 1.076083400767891 absolute error = 1.77635683940025e-15 relative error = 1.650761305427296e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.964 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.964 Order of pole (three term test) = 5.665e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9650000000000002 y[1] (closed_form) = 1.07385433165991 y[1] (numeric) = 1.073854331659908 absolute error = 1.554312234475219e-15 relative error = 1.447414410549187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.965 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.965 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9660000000000002 y[1] (closed_form) = 1.071632181543064 y[1] (numeric) = 1.071632181543063 absolute error = 1.77635683940025e-15 relative error = 1.657618042827381e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.966 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.966 Order of pole (three term test) = 6.029e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9670000000000002 y[1] (closed_form) = 1.06941692181172 y[1] (numeric) = 1.069416921811718 absolute error = 1.77635683940025e-15 relative error = 1.661051740597942e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.967 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.967 Order of pole (three term test) = 3.109e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9680000000000002 y[1] (closed_form) = 1.067208524007923 y[1] (numeric) = 1.067208524007921 absolute error = 1.77635683940025e-15 relative error = 1.664488991082181e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.968 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.968 Order of pole (three term test) = 3.207e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9690000000000002 y[1] (closed_form) = 1.065006959820482 y[1] (numeric) = 1.06500695982048 absolute error = 1.77635683940025e-15 relative error = 1.667929794280099e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.969 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.969 Order of pole (three term test) = 3.308e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9700000000000002 y[1] (closed_form) = 1.062812201084068 y[1] (numeric) = 1.062812201084066 absolute error = 1.77635683940025e-15 relative error = 1.671374150191696e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.97 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.97 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9710000000000002 y[1] (closed_form) = 1.060624219778308 y[1] (numeric) = 1.060624219778306 absolute error = 1.77635683940025e-15 relative error = 1.674822058816972e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.971 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.971 Order of pole (three term test) = 3.519e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9720000000000002 y[1] (closed_form) = 1.058442988026892 y[1] (numeric) = 1.058442988026891 absolute error = 1.554312234475219e-15 relative error = 1.468489330136436e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.972 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.972 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9730000000000002 y[1] (closed_form) = 1.056268478096688 y[1] (numeric) = 1.056268478096687 absolute error = 1.554312234475219e-15 relative error = 1.47151246743249e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.973 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.973 Order of pole (three term test) = 3.743e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9740000000000002 y[1] (closed_form) = 1.054100662396856 y[1] (numeric) = 1.054100662396854 absolute error = 1.554312234475219e-15 relative error = 1.474538713353014e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.974 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.974 Order of pole (three term test) = 7.721e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9750000000000002 y[1] (closed_form) = 1.051939513477975 y[1] (numeric) = 1.051939513477973 absolute error = 1.554312234475219e-15 relative error = 1.477568067898006e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.975 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.975 Order of pole (three term test) = 3.981e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9760000000000002 y[1] (closed_form) = 1.049785004031174 y[1] (numeric) = 1.049785004031172 absolute error = 1.332267629550188e-15 relative error = 1.269086169486401e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.976 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.976 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9770000000000002 y[1] (closed_form) = 1.047637106887271 y[1] (numeric) = 1.047637106887269 absolute error = 1.332267629550188e-15 relative error = 1.271688088166912e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.977 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.977 Order of pole (three term test) = 4.234e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9780000000000002 y[1] (closed_form) = 1.045495795015912 y[1] (numeric) = 1.045495795015911 absolute error = 1.554312234475219e-15 relative error = 1.486674783279796e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.978 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.978 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9790000000000002 y[1] (closed_form) = 1.043361041524726 y[1] (numeric) = 1.043361041524724 absolute error = 1.554312234475219e-15 relative error = 1.489716572322664e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.979 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.979 Order of pole (three term test) = 4.502e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9800000000000002 y[1] (closed_form) = 1.041232819658475 y[1] (numeric) = 1.041232819658474 absolute error = 1.554312234475219e-15 relative error = 1.492761469990001e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.98 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.98 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9810000000000002 y[1] (closed_form) = 1.039111102798222 y[1] (numeric) = 1.03911110279822 absolute error = 1.554312234475219e-15 relative error = 1.495809476281807e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.981 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.981 Order of pole (three term test) = 2.393e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9820000000000002 y[1] (closed_form) = 1.036995864460492 y[1] (numeric) = 1.03699586446049 absolute error = 1.554312234475219e-15 relative error = 1.498860591198082e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.982 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.982 Order of pole (three term test) = 4.934e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9830000000000002 y[1] (closed_form) = 1.034887078296451 y[1] (numeric) = 1.03488707829645 absolute error = 1.77635683940025e-15 relative error = 1.716474073987229e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.983 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.983 Order of pole (three term test) = 2.544e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9840000000000002 y[1] (closed_form) = 1.032784718091083 y[1] (numeric) = 1.032784718091081 absolute error = 1.554312234475219e-15 relative error = 1.504972146904038e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.984 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.984 Order of pole (three term test) = 5.245e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9850000000000002 y[1] (closed_form) = 1.030688757762374 y[1] (numeric) = 1.030688757762373 absolute error = 1.554312234475219e-15 relative error = 1.50803258769372e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.985 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.985 Order of pole (three term test) = 5.407e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9860000000000002 y[1] (closed_form) = 1.028599171360507 y[1] (numeric) = 1.028599171360506 absolute error = 1.554312234475219e-15 relative error = 1.511096137107871e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.986 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.986 Order of pole (three term test) = 2.787e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9870000000000002 y[1] (closed_form) = 1.026515933067055 y[1] (numeric) = 1.026515933067053 absolute error = 1.554312234475219e-15 relative error = 1.51416279514649e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.987 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.987 Order of pole (three term test) = 2.873e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9880000000000002 y[1] (closed_form) = 1.024439017194184 y[1] (numeric) = 1.024439017194183 absolute error = 1.332267629550188e-15 relative error = 1.300485052979639e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.988 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.988 Order of pole (three term test) = 5.924e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9890000000000002 y[1] (closed_form) = 1.022368398183864 y[1] (numeric) = 1.022368398183863 absolute error = 1.332267629550188e-15 relative error = 1.30311894608326e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.989 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.989 Order of pole (three term test) = 6.106e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9900000000000002 y[1] (closed_form) = 1.020304050607081 y[1] (numeric) = 1.020304050607079 absolute error = 1.554312234475219e-15 relative error = 1.523381421009163e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.99 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.99 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9910000000000002 y[1] (closed_form) = 1.018245949163052 y[1] (numeric) = 1.018245949163051 absolute error = 1.332267629550188e-15 relative error = 1.308394725896279e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.991 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.991 Order of pole (three term test) = 3.244e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9920000000000002 y[1] (closed_form) = 1.016194068678459 y[1] (numeric) = 1.016194068678458 absolute error = 1.332267629550188e-15 relative error = 1.311036612605677e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.992 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.992 Order of pole (three term test) = 3.344e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9930000000000002 y[1] (closed_form) = 1.014148384106672 y[1] (numeric) = 1.01414838410667 absolute error = 1.332267629550188e-15 relative error = 1.313681163850334e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.993 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.993 Order of pole (three term test) = 6.892e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9940000000000002 y[1] (closed_form) = 1.012108870526984 y[1] (numeric) = 1.012108870526983 absolute error = 1.332267629550188e-15 relative error = 1.31632837963025e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.994 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.994 Order of pole (three term test) = 7.104e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9950000000000002 y[1] (closed_form) = 1.01007550314386 y[1] (numeric) = 1.010075503143858 absolute error = 1.332267629550188e-15 relative error = 1.318978259945425e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.995 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.995 Order of pole (three term test) = 7.321e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9960000000000002 y[1] (closed_form) = 1.008048257286172 y[1] (numeric) = 1.008048257286171 absolute error = 1.332267629550188e-15 relative error = 1.32163080479586e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.996 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.996 Order of pole (three term test) = 3.773e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9970000000000002 y[1] (closed_form) = 1.006027108406463 y[1] (numeric) = 1.006027108406461 absolute error = 1.332267629550188e-15 relative error = 1.324286014181553e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.997 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.997 Order of pole (three term test) = 3.888e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9980000000000002 y[1] (closed_form) = 1.004012032080192 y[1] (numeric) = 1.004012032080191 absolute error = 1.332267629550188e-15 relative error = 1.326943888102506e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.998 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.998 Order of pole (three term test) = 4.007e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9990000000000002 y[1] (closed_form) = 1.002003004005006 y[1] (numeric) = 1.002003004005004 absolute error = 1.554312234475219e-15 relative error = 1.551205164318504e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 0.999 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.999 Order of pole (three term test) = 4.129e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1 y[1] (closed_form) = 0.9999999999999996 y[1] (numeric) = 0.9999999999999981 absolute error = 1.443289932012704e-15 relative error = 1.443289932012704e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1 Order of pole (three term test) = 4.255e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.001 y[1] (closed_form) = 0.9980029960049939 y[1] (numeric) = 0.9980029960049921 absolute error = 1.77635683940025e-15 relative error = 1.779911329435891e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.001 Order of pole (three term test) = 4.384e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.002 y[1] (closed_form) = 0.9960119680798084 y[1] (numeric) = 0.9960119680798065 absolute error = 1.887379141862766e-15 relative error = 1.894936207946785e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.002 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.002 Order of pole (three term test) = 4.517e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.003 y[1] (closed_form) = 0.9940268924035474 y[1] (numeric) = 0.9940268924035451 absolute error = 2.220446049250313e-15 relative error = 2.233788709560257e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.003 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.003 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.004 y[1] (closed_form) = 0.992047745273885 y[1] (numeric) = 0.9920477452738826 absolute error = 2.331468351712829e-15 relative error = 2.350157402020158e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.004 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.004 Order of pole (three term test) = 4.796e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.005 y[1] (closed_form) = 0.9900745031063595 y[1] (numeric) = 0.9900745031063568 absolute error = 2.664535259100376e-15 relative error = 2.691247225072855e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.005 Order of pole (three term test) = 4.941e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.006 y[1] (closed_form) = 0.9881071424336693 y[1] (numeric) = 0.9881071424336664 absolute error = 2.886579864025407e-15 relative error = 2.921322739268814e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.006 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.006 Order of pole (three term test) = 7.636e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.006999999999999 y[1] (closed_form) = 0.9861456399049762 y[1] (numeric) = 0.9861456399049731 absolute error = 3.108624468950438e-15 relative error = 3.152297534114719e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.007 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.007 Order of pole (three term test) = 2.622e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.007999999999999 y[1] (closed_form) = 0.9841899722852118 y[1] (numeric) = 0.9841899722852084 absolute error = 3.33066907387547e-15 relative error = 3.384172941878201e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.008 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.008 Order of pole (three term test) = 5.403e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.008999999999999 y[1] (closed_form) = 0.9822401164543897 y[1] (numeric) = 0.9822401164543862 absolute error = 3.441691376337985e-15 relative error = 3.503920598113547e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.009 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.009 Order of pole (three term test) = 2.783e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.009999999999999 y[1] (closed_form) = 0.9802960494069226 y[1] (numeric) = 0.9802960494069189 absolute error = 3.663735981263017e-15 relative error = 3.737377074486397e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.01 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.01 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.010999999999999 y[1] (closed_form) = 0.9783577482509428 y[1] (numeric) = 0.978357748250939 absolute error = 3.774758283725532e-15 relative error = 3.858259711719817e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.011 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.011 Order of pole (three term test) = 5.907e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.011999999999999 y[1] (closed_form) = 0.9764251902076292 y[1] (numeric) = 0.9764251902076251 absolute error = 4.107825191113079e-15 relative error = 4.207004522527304e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.012 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.012 Order of pole (three term test) = 6.085e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.012999999999999 y[1] (closed_form) = 0.9744983526105372 y[1] (numeric) = 0.974498352610533 absolute error = 4.218847493575595e-15 relative error = 4.329250513634964e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.013 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.013 Order of pole (three term test) = 9.402e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.013999999999999 y[1] (closed_form) = 0.972577212904935 y[1] (numeric) = 0.9725772129049306 absolute error = 4.440892098500626e-15 relative error = 4.566107492109938e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.014 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.014 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.014999999999999 y[1] (closed_form) = 0.9706617486471428 y[1] (numeric) = 0.9706617486471383 absolute error = 4.551914400963142e-15 relative error = 4.68949601373224e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.015 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.015 Order of pole (three term test) = 6.65e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.015999999999998 y[1] (closed_form) = 0.9687519375038779 y[1] (numeric) = 0.9687519375038731 absolute error = 4.773959005888173e-15 relative error = 4.927947827582087e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.016 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.016 Order of pole (three term test) = 3.425e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.016999999999998 y[1] (closed_form) = 0.9668477572516031 y[1] (numeric) = 0.966847757251598 absolute error = 5.10702591327572e-15 relative error = 5.282140724816013e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.017 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.017 Order of pole (three term test) = 3.527e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.017999999999998 y[1] (closed_form) = 0.9649491857758803 y[1] (numeric) = 0.9649491857758752 absolute error = 5.10702591327572e-15 relative error = 5.292533522549529e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.018 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.018 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.018999999999998 y[1] (closed_form) = 0.9630562010707294 y[1] (numeric) = 0.963056201070724 absolute error = 5.440092820663267e-15 relative error = 5.64878022135671e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.019 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.019 Order of pole (three term test) = 7.483e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.019999999999998 y[1] (closed_form) = 0.9611687812379892 y[1] (numeric) = 0.9611687812379834 absolute error = 5.773159728050814e-15 relative error = 6.006395381064043e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.02 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.02 Order of pole (three term test) = 3.853e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.020999999999998 y[1] (closed_form) = 0.9592869044866847 y[1] (numeric) = 0.9592869044866789 absolute error = 5.88418203051333e-15 relative error = 6.13391260007032e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.021 Order of pole (three term test) = 3.968e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.021999999999998 y[1] (closed_form) = 0.9574105491323986 y[1] (numeric) = 0.9574105491323927 absolute error = 5.995204332975845e-15 relative error = 6.261895002523916e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.022 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.022 Order of pole (three term test) = 8.173e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.022999999999998 y[1] (closed_form) = 0.9555396935966461 y[1] (numeric) = 0.9555396935966399 absolute error = 6.217248937900877e-15 relative error = 6.506531313732437e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.023 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.023 Order of pole (three term test) = 4.208e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.023999999999998 y[1] (closed_form) = 0.9536743164062546 y[1] (numeric) = 0.9536743164062481 absolute error = 6.439293542825908e-15 relative error = 6.752088665962187e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.024 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.024 Order of pole (three term test) = 4.333e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.024999999999997 y[1] (closed_form) = 0.9518143961927471 y[1] (numeric) = 0.9518143961927406 absolute error = 6.550315845288424e-15 relative error = 6.881925584956116e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.025 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.025 Order of pole (three term test) = 8.924e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.025999999999997 y[1] (closed_form) = 0.9499599116917314 y[1] (numeric) = 0.9499599116917248 absolute error = 6.661338147750939e-15 relative error = 7.012230796021832e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.026 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.026999999999997 y[1] (closed_form) = 0.9481108417422915 y[1] (numeric) = 0.9481108417422845 absolute error = 6.994405055138486e-15 relative error = 7.37720184940112e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.027 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.027 Order of pole (three term test) = 2.365e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.027999999999997 y[1] (closed_form) = 0.9462671652863837 y[1] (numeric) = 0.9462671652863764 absolute error = 7.216449660063518e-15 relative error = 7.626228537560521e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.028 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.028 Order of pole (three term test) = 4.871e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.028999999999997 y[1] (closed_form) = 0.9444288613682373 y[1] (numeric) = 0.94442886136823 absolute error = 7.327471962526033e-15 relative error = 7.758627740272983e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.029 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.029 Order of pole (three term test) = 2.508e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.029999999999997 y[1] (closed_form) = 0.94259590913376 y[1] (numeric) = 0.9425959091337525 absolute error = 7.549516567451064e-15 relative error = 8.009282126408787e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.03 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.03 Order of pole (three term test) = 7.745e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.030999999999997 y[1] (closed_form) = 0.940768287829945 y[1] (numeric) = 0.9407682878299373 absolute error = 7.771561172376096e-15 relative error = 8.260866435350015e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.031 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.031 Order of pole (three term test) = 2.658e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.031999999999997 y[1] (closed_form) = 0.9389459768042846 y[1] (numeric) = 0.9389459768042766 absolute error = 7.993605777301127e-15 relative error = 8.513381999364301e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.032 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.032 Order of pole (three term test) = 5.473e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.032999999999997 y[1] (closed_form) = 0.9371289555041863 y[1] (numeric) = 0.9371289555041781 absolute error = 8.215650382226158e-15 relative error = 8.766830150719271e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.033 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.033 Order of pole (three term test) = 2.817e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.033999999999996 y[1] (closed_form) = 0.9353172034763934 y[1] (numeric) = 0.9353172034763849 absolute error = 8.43769498715119e-15 relative error = 9.021212221682556e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.034 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.034 Order of pole (three term test) = 5.8e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.034999999999996 y[1] (closed_form) = 0.9335107003664095 y[1] (numeric) = 0.9335107003664008 absolute error = 8.659739592076221e-15 relative error = 9.276529544521786e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.035 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.035 Order of pole (three term test) = 8.956e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.035999999999996 y[1] (closed_form) = 0.9317094259179269 y[1] (numeric) = 0.9317094259179179 absolute error = 8.992806499463768e-15 relative error = 9.651943244648393e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.036 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.036 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.036999999999996 y[1] (closed_form) = 0.9299133599722583 y[1] (numeric) = 0.9299133599722492 absolute error = 9.103828801926284e-15 relative error = 9.789975274898592e-13 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 15 h = -0.001 Radius of convergence (given) for eq 1 = 1.037 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.037 Order of pole (three term test) = 6.327e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.037999999999996 y[1] (closed_form) = 0.9281224824677734 y[1] (numeric) = 0.9281224824677641 absolute error = 9.325873406851315e-15 relative error = 1.004810634697143e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.038 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.038 Order of pole (three term test) = 3.256e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.038999999999996 y[1] (closed_form) = 0.9263367734393383 y[1] (numeric) = 0.9263367734393287 absolute error = 9.547918011776346e-15 relative error = 1.030717799999073e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.039 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.039 Order of pole (three term test) = 3.352e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.039999999999996 y[1] (closed_form) = 0.9245562130177589 y[1] (numeric) = 0.9245562130177493 absolute error = 9.658940314238862e-15 relative error = 1.044710984388067e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.04 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.04 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.040999999999996 y[1] (closed_form) = 0.922780781429229 y[1] (numeric) = 0.922780781429219 absolute error = 9.992007221626409e-15 relative error = 1.082814837793924e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.041 Order of pole (three term test) = 7.101e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.041999999999996 y[1] (closed_form) = 0.9210104589947802 y[1] (numeric) = 0.9210104589947701 absolute error = 1.010302952408892e-14 relative error = 1.096950574819279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.042 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.042 Order of pole (three term test) = 3.654e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.042999999999995 y[1] (closed_form) = 0.9192452261297374 y[1] (numeric) = 0.9192452261297271 absolute error = 1.021405182655144e-14 relative error = 1.111134606546206e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.043 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.043 Order of pole (three term test) = 3.761e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.043999999999995 y[1] (closed_form) = 0.9174850633431768 y[1] (numeric) = 0.9174850633431665 absolute error = 1.032507412901396e-14 relative error = 1.125366999588086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.044 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.044 Order of pole (three term test) = 3.871e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.044999999999995 y[1] (closed_form) = 0.9157299512373884 y[1] (numeric) = 0.9157299512373778 absolute error = 1.06581410364015e-14 relative error = 1.163895646527624e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.045 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.045 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.045999999999995 y[1] (closed_form) = 0.9139798705073404 y[1] (numeric) = 0.9139798705073297 absolute error = 1.076916333886402e-14 relative error = 1.178271391566443e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.046 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.046 Order of pole (three term test) = 4.1e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.046999999999995 y[1] (closed_form) = 0.9122348019401496 y[1] (numeric) = 0.9122348019401386 absolute error = 1.099120794378905e-14 relative error = 1.204866106885294e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.047 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.047 Order of pole (three term test) = 4.219e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.047999999999995 y[1] (closed_form) = 0.9104947264145534 y[1] (numeric) = 0.9104947264145422 absolute error = 1.121325254871408e-14 relative error = 1.231556012726275e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.048 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.048 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.048999999999995 y[1] (closed_form) = 0.9087596249003862 y[1] (numeric) = 0.9087596249003748 absolute error = 1.143529715363911e-14 relative error = 1.258341242316151e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.049 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.049 Order of pole (three term test) = 4.467e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.049999999999995 y[1] (closed_form) = 0.907029478458059 y[1] (numeric) = 0.9070294784580474 absolute error = 1.165734175856414e-14 relative error = 1.285221928881684e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.05 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.05 Order of pole (three term test) = 4.597e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.050999999999995 y[1] (closed_form) = 0.9053042682380428 y[1] (numeric) = 0.9053042682380309 absolute error = 1.187938636348917e-14 relative error = 1.312198205649637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.051 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.051 Order of pole (three term test) = 2.365e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.051999999999994 y[1] (closed_form) = 0.9035839754803547 y[1] (numeric) = 0.9035839754803426 absolute error = 1.210143096841421e-14 relative error = 1.339270205846773e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.052 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.052 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.052999999999994 y[1] (closed_form) = 0.9018685815140486 y[1] (numeric) = 0.9018685815140363 absolute error = 1.232347557333924e-14 relative error = 1.366438062699856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.053 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.053 Order of pole (three term test) = 5.008e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.053999999999994 y[1] (closed_form) = 0.9001580677567079 y[1] (numeric) = 0.9001580677566954 absolute error = 1.254552017826427e-14 relative error = 1.393701909435648e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.054 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 Order of pole (three term test) = 2.576e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.054999999999994 y[1] (closed_form) = 0.8984524157139426 y[1] (numeric) = 0.89845241571393 absolute error = 1.265654248072678e-14 relative error = 1.408704819461077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.055 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.055 Order of pole (three term test) = 2.651e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.055999999999994 y[1] (closed_form) = 0.8967516069788899 y[1] (numeric) = 0.8967516069788769 absolute error = 1.298960938811433e-14 relative error = 1.44851810546241e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.056 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.056 Order of pole (three term test) = 5.454e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.056999999999994 y[1] (closed_form) = 0.8950556232317159 y[1] (numeric) = 0.8950556232317028 absolute error = 1.310063169057685e-14 relative error = 1.463666765566513e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.057 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.057 Order of pole (three term test) = 2.806e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.057999999999994 y[1] (closed_form) = 0.8933644462391247 y[1] (numeric) = 0.8933644462391115 absolute error = 1.321165399303936e-14 relative error = 1.478864986026434e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.058 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.058 Order of pole (three term test) = 2.886e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.058999999999994 y[1] (closed_form) = 0.8916780578538663 y[1] (numeric) = 0.8916780578538529 absolute error = 1.343369859796439e-14 relative error = 1.506563773734353e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.059 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.059 Order of pole (three term test) = 2.969e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.059999999999994 y[1] (closed_form) = 0.8899964400142507 y[1] (numeric) = 0.8899964400142371 absolute error = 1.365574320288943e-14 relative error = 1.534359306276637e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.06 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.06 Order of pole (three term test) = 3.054e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.060999999999994 y[1] (closed_form) = 0.8883195747436641 y[1] (numeric) = 0.8883195747436503 absolute error = 1.376676550535194e-14 relative error = 1.54975370314501e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.061 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.061 Order of pole (three term test) = 3.142e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.061999999999993 y[1] (closed_form) = 0.8866474441500884 y[1] (numeric) = 0.8866474441500746 absolute error = 1.387778780781446e-14 relative error = 1.56519797123165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.062 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.062 Order of pole (three term test) = 3.232e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.062999999999993 y[1] (closed_form) = 0.8849800304256247 y[1] (numeric) = 0.8849800304256105 absolute error = 1.4210854715202e-14 relative error = 1.605782529168189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.063 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.063 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.063999999999993 y[1] (closed_form) = 0.8833173158460172 y[1] (numeric) = 0.8833173158460029 absolute error = 1.432187701766452e-14 relative error = 1.621373968418973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.064 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.064 Order of pole (three term test) = 6.84e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.064999999999993 y[1] (closed_form) = 0.8816592827701849 y[1] (numeric) = 0.8816592827701704 absolute error = 1.454392162258955e-14 relative error = 1.649607950238142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.065 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.065 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.065999999999993 y[1] (closed_form) = 0.8800059136397513 y[1] (numeric) = 0.8800059136397366 absolute error = 1.476596622751458e-14 relative error = 1.677939431843334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.066 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.066 Order of pole (three term test) = 7.236e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.066999999999993 y[1] (closed_form) = 0.8783571909785808 y[1] (numeric) = 0.8783571909785658 absolute error = 1.498801083243961e-14 relative error = 1.706368546461311e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.067 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.067 Order of pole (three term test) = 3.721e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.067999999999993 y[1] (closed_form) = 0.8767130973923165 y[1] (numeric) = 0.8767130973923014 absolute error = 1.509903313490213e-14 relative error = 1.722231957046437e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.068 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.068 Order of pole (three term test) = 7.655e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.068999999999993 y[1] (closed_form) = 0.8750736155679217 y[1] (numeric) = 0.8750736155679064 absolute error = 1.532107773982716e-14 relative error = 1.750833011904238e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.069 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.069 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.069999999999993 y[1] (closed_form) = 0.8734387282732239 y[1] (numeric) = 0.8734387282732083 absolute error = 1.554312234475219e-14 relative error = 1.779532077250653e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.07 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.07 Order of pole (three term test) = 4.048e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.070999999999992 y[1] (closed_form) = 0.8718084183564617 y[1] (numeric) = 0.871808418356446 absolute error = 1.576516694967722e-14 relative error = 1.808329286312446e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.071 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.071 Order of pole (three term test) = 4.163e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.071999999999992 y[1] (closed_form) = 0.8701826687458356 y[1] (numeric) = 0.8701826687458197 absolute error = 1.587618925213974e-14 relative error = 1.824466266953069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.072 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.072 Order of pole (three term test) = 8.563e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.072999999999992 y[1] (closed_form) = 0.8685614624490607 y[1] (numeric) = 0.8685614624490446 absolute error = 1.609823385706477e-14 relative error = 1.853436348842025e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.073 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.073 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.073999999999992 y[1] (closed_form) = 0.8669447825529225 y[1] (numeric) = 0.8669447825529062 absolute error = 1.63202784619898e-14 relative error = 1.882504951922187e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.074 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.074 Order of pole (three term test) = 4.528e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.074999999999992 y[1] (closed_form) = 0.8653326122228361 y[1] (numeric) = 0.8653326122228197 absolute error = 1.643130076445232e-14 relative error = 1.898842194591993e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.075 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.075 Order of pole (three term test) = 6.984e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.075999999999992 y[1] (closed_form) = 0.863724934702408 y[1] (numeric) = 0.8637249347023914 absolute error = 1.654232306691483e-14 relative error = 1.91523046311201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.076 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.076 Order of pole (three term test) = 2.394e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.076999999999992 y[1] (closed_form) = 0.8621217333130005 y[1] (numeric) = 0.8621217333129837 absolute error = 1.676436767183986e-14 relative error = 1.944547622922925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.077 Order of pole (three term test) = 2.462e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.077999999999992 y[1] (closed_form) = 0.860522991453299 y[1] (numeric) = 0.860522991453282 absolute error = 1.69864122767649e-14 relative error = 1.973963792423175e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.078 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.078 Order of pole (three term test) = 5.062e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.078999999999992 y[1] (closed_form) = 0.8589286925988826 y[1] (numeric) = 0.8589286925988655 absolute error = 1.709743457922741e-14 relative error = 1.990553433195399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.079 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.079 Order of pole (three term test) = 2.602e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.079999999999991 y[1] (closed_form) = 0.8573388203017969 y[1] (numeric) = 0.8573388203017795 absolute error = 1.731947918415244e-14 relative error = 2.020144052039509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.08 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.08 Order of pole (three term test) = 2.676e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.080999999999991 y[1] (closed_form) = 0.8557533581901297 y[1] (numeric) = 0.8557533581901121 absolute error = 1.754152378907747e-14 relative error = 2.049834058048783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.081 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.081999999999991 y[1] (closed_form) = 0.8541722899675895 y[1] (numeric) = 0.8541722899675718 absolute error = 1.77635683940025e-14 relative error = 2.079623584449985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.082 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.082 Order of pole (three term test) = 8.485e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.082999999999991 y[1] (closed_form) = 0.8525955994130873 y[1] (numeric) = 0.8525955994130693 absolute error = 1.798561299892754e-14 relative error = 2.109512764469877e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.083 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.083 Order of pole (three term test) = 2.908e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.083999999999991 y[1] (closed_form) = 0.8510232703803194 y[1] (numeric) = 0.8510232703803013 absolute error = 1.809663530139005e-14 relative error = 2.126455989070984e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.084 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.084 Order of pole (three term test) = 2.99e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.084999999999991 y[1] (closed_form) = 0.8494552867973555 y[1] (numeric) = 0.8494552867973373 absolute error = 1.820765760385257e-14 relative error = 2.143450972269498e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.085 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.085 Order of pole (three term test) = 3.073e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.085999999999991 y[1] (closed_form) = 0.8478916326662267 y[1] (numeric) = 0.8478916326662083 absolute error = 1.84297022087776e-14 relative error = 2.173591706622309e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.086 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.086 Order of pole (three term test) = 3.16e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.086999999999991 y[1] (closed_form) = 0.8463322920625179 y[1] (numeric) = 0.8463322920624994 absolute error = 1.854072451124011e-14 relative error = 2.190714532002109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.087 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.087 Order of pole (three term test) = 3.248e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.087999999999991 y[1] (closed_form) = 0.8447772491349628 y[1] (numeric) = 0.8447772491349441 absolute error = 1.865174681370263e-14 relative error = 2.207889338023922e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.088 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.088 Order of pole (three term test) = 3.339e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.08899999999999 y[1] (closed_form) = 0.8432264881050404 y[1] (numeric) = 0.8432264881050215 absolute error = 1.887379141862766e-14 relative error = 2.238282559296994e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.089 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.089 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.08999999999999 y[1] (closed_form) = 0.8416799932665751 y[1] (numeric) = 0.841679993266556 absolute error = 1.909583602355269e-14 relative error = 2.268776277958255e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.09 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.09 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09099999999999 y[1] (closed_form) = 0.8401377489853388 y[1] (numeric) = 0.8401377489853195 absolute error = 1.931788062847772e-14 relative error = 2.299370627234468e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.091 Order of pole (three term test) = 3.626e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09199999999999 y[1] (closed_form) = 0.838599739698656 y[1] (numeric) = 0.8385997396986365 absolute error = 1.942890293094024e-14 relative error = 2.31682673046403e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.092 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.092 Order of pole (three term test) = 3.727e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09299999999999 y[1] (closed_form) = 0.8370659499150113 y[1] (numeric) = 0.8370659499149916 absolute error = 1.965094753586527e-14 relative error = 2.347598482277348e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.093 Order of pole (three term test) = 3.831e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09399999999999 y[1] (closed_form) = 0.8355363642136587 y[1] (numeric) = 0.835536364213639 absolute error = 1.976196983832779e-14 relative error = 2.365183693342444e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.094 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.094 Order of pole (three term test) = 3.938e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09499999999999 y[1] (closed_form) = 0.8340109672442348 y[1] (numeric) = 0.8340109672442149 absolute error = 1.998401444325282e-14 relative error = 2.396133291782076e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.095 Order of pole (three term test) = 1.214e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09599999999999 y[1] (closed_form) = 0.8324897437263731 y[1] (numeric) = 0.8324897437263529 absolute error = 2.020605904817785e-14 relative error = 2.427184142561554e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.096 Order of pole (three term test) = 4.16e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.09699999999999 y[1] (closed_form) = 0.8309726784493211 y[1] (numeric) = 0.8309726784493008 absolute error = 2.031708135064036e-14 relative error = 2.44497585510923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.097 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.097 Order of pole (three term test) = 4.275e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.097999999999989 y[1] (closed_form) = 0.8294597562715612 y[1] (numeric) = 0.8294597562715407 absolute error = 2.05391259555654e-14 relative error = 2.476205240853299e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.098 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.098999999999989 y[1] (closed_form) = 0.8279509621204316 y[1] (numeric) = 0.827950962120411 absolute error = 2.065014825802791e-14 relative error = 2.494126971619389e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.099 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.099 Order of pole (three term test) = 9.03e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.099999999999989 y[1] (closed_form) = 0.8264462809917518 y[1] (numeric) = 0.8264462809917309 absolute error = 2.087219286295294e-14 relative error = 2.525535336417256e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.1 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.1 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.100999999999989 y[1] (closed_form) = 0.8249456979494488 y[1] (numeric) = 0.8249456979494278 absolute error = 2.098321516541546e-14 relative error = 2.543587440673128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.101 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.101 Order of pole (three term test) = 2.384e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.101999999999989 y[1] (closed_form) = 0.8234491981251874 y[1] (numeric) = 0.8234491981251661 absolute error = 2.120525977034049e-14 relative error = 2.575175228614006e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.102 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.102 Order of pole (three term test) = 1.225e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.102999999999989 y[1] (closed_form) = 0.8219567667180008 y[1] (numeric) = 0.8219567667179795 absolute error = 2.131628207280301e-14 relative error = 2.593358061631027e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.103 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.103 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.103999999999989 y[1] (closed_form) = 0.8204683889939256 y[1] (numeric) = 0.8204683889939041 absolute error = 2.153832667772804e-14 relative error = 2.625125716804124e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.104 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.104 Order of pole (three term test) = 5.174e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.104999999999989 y[1] (closed_form) = 0.8189840502856376 y[1] (numeric) = 0.8189840502856158 absolute error = 2.176037128265307e-14 relative error = 2.656995734540091e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.105 Order of pole (three term test) = 2.658e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.105999999999989 y[1] (closed_form) = 0.8175037359920904 y[1] (numeric) = 0.8175037359920686 absolute error = 2.176037128265307e-14 relative error = 2.661806952630686e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.106 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.106 Order of pole (three term test) = 2.731e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.106999999999988 y[1] (closed_form) = 0.8160274315781569 y[1] (numeric) = 0.816027431578135 absolute error = 2.19824158875781e-14 relative error = 2.693832956701613e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.107 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.107 Order of pole (three term test) = 2.806e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.107999999999988 y[1] (closed_form) = 0.814555122574272 y[1] (numeric) = 0.8145551225742498 absolute error = 2.220446049250313e-14 relative error = 2.725961678606779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.108 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.108 Order of pole (three term test) = 8.65e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.108999999999988 y[1] (closed_form) = 0.8130867945760779 y[1] (numeric) = 0.8130867945760555 absolute error = 2.242650509742816e-14 relative error = 2.758193251572946e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.109 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.109999999999988 y[1] (closed_form) = 0.8116224332440722 y[1] (numeric) = 0.8116224332440497 absolute error = 2.253752739989068e-14 relative error = 2.776848750940471e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.11 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.11 Order of pole (three term test) = 3.044e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.110999999999988 y[1] (closed_form) = 0.8101620243032579 y[1] (numeric) = 0.8101620243032351 absolute error = 2.275957200481571e-14 relative error = 2.809261767655553e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.111 Order of pole (three term test) = 3.127e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.111999999999988 y[1] (closed_form) = 0.8087055535427949 y[1] (numeric) = 0.808705553542772 absolute error = 2.298161660974074e-14 relative error = 2.841778012907463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.112 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.112 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.112999999999988 y[1] (closed_form) = 0.8072530068156549 y[1] (numeric) = 0.8072530068156317 absolute error = 2.320366121466577e-14 relative error = 2.874397619922967e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.113 Order of pole (three term test) = 6.601e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.113999999999988 y[1] (closed_form) = 0.8058043700382774 y[1] (numeric) = 0.8058043700382541 absolute error = 2.331468351712829e-14 relative error = 2.89334289860215e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.114 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.114 Order of pole (three term test) = 1.017e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.114999999999988 y[1] (closed_form) = 0.804359629190229 y[1] (numeric) = 0.8043596291902054 absolute error = 2.353672812205332e-14 relative error = 2.926144881953908e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.115 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.115 Order of pole (three term test) = 6.966e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.115999999999987 y[1] (closed_form) = 0.8029187703138629 y[1] (numeric) = 0.8029187703138393 absolute error = 2.364775042451583e-14 relative error = 2.945223265271513e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.116 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.116 Order of pole (three term test) = 3.578e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.116999999999987 y[1] (closed_form) = 0.8014817795139836 y[1] (numeric) = 0.8014817795139598 absolute error = 2.375877272697835e-14 relative error = 2.964355938495022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.117 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.117 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.117999999999987 y[1] (closed_form) = 0.8000486429575101 y[1] (numeric) = 0.8000486429574861 absolute error = 2.398081733190338e-14 relative error = 2.997419912276132e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.118 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.118 Order of pole (three term test) = 7.551e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.118999999999987 y[1] (closed_form) = 0.7986193468731442 y[1] (numeric) = 0.79861934687312 absolute error = 2.420286193682841e-14 relative error = 3.03058798056803e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.119 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.119 Order of pole (three term test) = 3.878e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.119999999999987 y[1] (closed_form) = 0.7971938775510389 y[1] (numeric) = 0.7971938775510146 absolute error = 2.431388423929093e-14 relative error = 3.049933638976583e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.12 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.12 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.120999999999987 y[1] (closed_form) = 0.7957722213424704 y[1] (numeric) = 0.795772221342446 absolute error = 2.442490654175344e-14 relative error = 3.069333898153487e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.121 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.121 Order of pole (three term test) = 4.091e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.121999999999987 y[1] (closed_form) = 0.7943543646595108 y[1] (numeric) = 0.7943543646594862 absolute error = 2.464695114667848e-14 relative error = 3.102765244733445e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.122 Order of pole (three term test) = 8.405e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.122999999999987 y[1] (closed_form) = 0.7929402939747034 y[1] (numeric) = 0.7929402939746787 absolute error = 2.475797344914099e-14 relative error = 3.122299829794099e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.123 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.123 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.123999999999987 y[1] (closed_form) = 0.7915299958207406 y[1] (numeric) = 0.7915299958207157 absolute error = 2.486899575160351e-14 relative error = 3.141889237667708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.124 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.124 Order of pole (three term test) = 4.433e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.124999999999986 y[1] (closed_form) = 0.7901234567901425 y[1] (numeric) = 0.7901234567901175 absolute error = 2.498001805406602e-14 relative error = 3.161533534967655e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.125 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.125 Order of pole (three term test) = 4.553e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.125999999999986 y[1] (closed_form) = 0.788720663534939 y[1] (numeric) = 0.7887206635349139 absolute error = 2.509104035652854e-14 relative error = 3.18123278830732e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.126 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.126 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.126999999999986 y[1] (closed_form) = 0.7873216027663524 y[1] (numeric) = 0.7873216027663272 absolute error = 2.520206265899105e-14 relative error = 3.200987064300086e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.127 Order of pole (three term test) = 9.604e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.127999999999986 y[1] (closed_form) = 0.7859262612544834 y[1] (numeric) = 0.7859262612544581 absolute error = 2.531308496145357e-14 relative error = 3.220796429559334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.128 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.128 Order of pole (three term test) = 9.863e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.128999999999986 y[1] (closed_form) = 0.7845346258279977 y[1] (numeric) = 0.7845346258279722 absolute error = 2.55351295663786e-14 relative error = 3.254812308561758e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.129 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.129 Order of pole (three term test) = 2.532e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.129999999999986 y[1] (closed_form) = 0.7831466833738154 y[1] (numeric) = 0.7831466833737898 absolute error = 2.564615186884112e-14 relative error = 3.27475713213224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.13 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.13 Order of pole (three term test) = 2.6e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.130999999999986 y[1] (closed_form) = 0.7817624208368025 y[1] (numeric) = 0.7817624208367767 absolute error = 2.575717417130363e-14 relative error = 3.29475726701381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.131 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.131 Order of pole (three term test) = 2.67e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.131999999999986 y[1] (closed_form) = 0.7803818252194631 y[1] (numeric) = 0.7803818252194372 absolute error = 2.586819647376615e-14 relative error = 3.314812779819847e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.132 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.132 Order of pole (three term test) = 5.484e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.132999999999986 y[1] (closed_form) = 0.779004883581635 y[1] (numeric) = 0.779004883581609 absolute error = 2.597921877622866e-14 relative error = 3.334923737163735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.133 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.133 Order of pole (three term test) = 5.631e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.133999999999985 y[1] (closed_form) = 0.7776315830401861 y[1] (numeric) = 0.77763158304016 absolute error = 2.609024107869118e-14 relative error = 3.355090205658854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.134 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.134 Order of pole (three term test) = 5.782e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.134999999999985 y[1] (closed_form) = 0.7762619107687134 y[1] (numeric) = 0.7762619107686871 absolute error = 2.631228568361621e-14 relative error = 3.389614422477561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.135 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.135 Order of pole (three term test) = 8.906e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.135999999999985 y[1] (closed_form) = 0.7748958539972429 y[1] (numeric) = 0.7748958539972165 absolute error = 2.642330798607873e-14 relative error = 3.409917326280176e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.136 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.136 Order of pole (three term test) = 3.048e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.136999999999985 y[1] (closed_form) = 0.7735334000119326 y[1] (numeric) = 0.7735334000119061 absolute error = 2.653433028854124e-14 relative error = 3.430275963278628e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.137 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.137 Order of pole (three term test) = 3.13e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.137999999999985 y[1] (closed_form) = 0.7721745361547764 y[1] (numeric) = 0.7721745361547497 absolute error = 2.664535259100376e-14 relative error = 3.450690400086297e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.138 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.138 Order of pole (three term test) = 6.426e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.138999999999985 y[1] (closed_form) = 0.7708192498233101 y[1] (numeric) = 0.7708192498232832 absolute error = 2.686739719592879e-14 relative error = 3.485563859761861e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.139 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.139 Order of pole (three term test) = 3.299e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.139999999999985 y[1] (closed_form) = 0.7694675284703191 y[1] (numeric) = 0.769467528470292 absolute error = 2.708944180085382e-14 relative error = 3.520543856438868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.14 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.14 Order of pole (three term test) = 1.016e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.140999999999985 y[1] (closed_form) = 0.7681193596035482 y[1] (numeric) = 0.7681193596035208 absolute error = 2.731148640577885e-14 relative error = 3.555630523344082e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.141 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.141 Order of pole (three term test) = 6.955e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.141999999999985 y[1] (closed_form) = 0.7667747307854127 y[1] (numeric) = 0.7667747307853853 absolute error = 2.742250870824137e-14 relative error = 3.576344864697393e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.142 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.142 Order of pole (three term test) = 3.57e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.142999999999984 y[1] (closed_form) = 0.7654336296327122 y[1] (numeric) = 0.7654336296326846 absolute error = 2.76445533131664e-14 relative error = 3.611619903143194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.143 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.143 Order of pole (three term test) = 3.665e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.143999999999984 y[1] (closed_form) = 0.7640960438163444 y[1] (numeric) = 0.7640960438163167 absolute error = 2.775557561562891e-14 relative error = 3.632472100889473e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.144 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.144 Order of pole (three term test) = 3.762e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.144999999999984 y[1] (closed_form) = 0.7627619610610229 y[1] (numeric) = 0.762761961060995 absolute error = 2.786659791809143e-14 relative error = 3.653380653556481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.145 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.145 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.145999999999984 y[1] (closed_form) = 0.7614313691449945 y[1] (numeric) = 0.7614313691449666 absolute error = 2.797762022055394e-14 relative error = 3.674345627757601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.146 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.146 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.146999999999984 y[1] (closed_form) = 0.7601042558997604 y[1] (numeric) = 0.7601042558997322 absolute error = 2.819966482547898e-14 relative error = 3.709973284138254e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.147 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.147 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.147999999999984 y[1] (closed_form) = 0.7587806092097967 y[1] (numeric) = 0.7587806092097684 absolute error = 2.831068712794149e-14 relative error = 3.731076780866156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.148 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.148 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.148999999999984 y[1] (closed_form) = 0.7574604170122794 y[1] (numeric) = 0.7574604170122509 absolute error = 2.853273173286652e-14 relative error = 3.766894096646105e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.149 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.149 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.149999999999984 y[1] (closed_form) = 0.7561436672968078 y[1] (numeric) = 0.7561436672967792 absolute error = 2.864375403532904e-14 relative error = 3.788136471172158e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.15 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.15 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.150999999999984 y[1] (closed_form) = 0.7548303481051332 y[1] (numeric) = 0.7548303481051044 absolute error = 2.875477633779155e-14 relative error = 3.80943564470815e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.151 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.151 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.151999999999983 y[1] (closed_form) = 0.7535204475308858 y[1] (numeric) = 0.7535204475308569 absolute error = 2.886579864025407e-14 relative error = 3.830791683867464e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.152 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.152 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.152999999999983 y[1] (closed_form) = 0.752213953719306 y[1] (numeric) = 0.7522139537192769 absolute error = 2.90878432451791e-14 relative error = 3.866964060072919e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.153 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.153 Order of pole (three term test) = 2.38e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.153999999999983 y[1] (closed_form) = 0.7509108548669754 y[1] (numeric) = 0.7509108548669462 absolute error = 2.919886554764162e-14 relative error = 3.888459643164198e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.154 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.154 Order of pole (three term test) = 4.885e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.154999999999983 y[1] (closed_form) = 0.7496111392215508 y[1] (numeric) = 0.7496111392215213 absolute error = 2.942091015256665e-14 relative error = 3.924822966627657e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.155 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.155 Order of pole (three term test) = 5.013e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.155999999999983 y[1] (closed_form) = 0.7483147950814985 y[1] (numeric) = 0.7483147950814689 absolute error = 2.953193245502916e-14 relative error = 3.946458448922269e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.156 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.156 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.156999999999983 y[1] (closed_form) = 0.7470218107958319 y[1] (numeric) = 0.7470218107958021 absolute error = 2.97539770599542e-14 relative error = 3.983013163732944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.157 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.157 Order of pole (three term test) = 2.64e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.157999999999983 y[1] (closed_form) = 0.7457321747638487 y[1] (numeric) = 0.7457321747638188 absolute error = 2.986499936241671e-14 relative error = 4.004788900502258e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.158 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.158 Order of pole (three term test) = 5.419e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.158999999999983 y[1] (closed_form) = 0.7444458754348716 y[1] (numeric) = 0.7444458754348415 absolute error = 3.008704396734174e-14 relative error = 4.041535450749358e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.159 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.159 Order of pole (three term test) = 2.781e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.159999999999983 y[1] (closed_form) = 0.743162901307989 y[1] (numeric) = 0.7431629013079587 absolute error = 3.030908857226677e-14 relative error = 4.078390958284095e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.16 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 Order of pole (three term test) = 2.854e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.160999999999982 y[1] (closed_form) = 0.7418832409317981 y[1] (numeric) = 0.7418832409317676 absolute error = 3.05311331771918e-14 relative error = 4.115355556333231e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.161 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.161 Order of pole (three term test) = 5.857e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.161999999999982 y[1] (closed_form) = 0.7406068829041493 y[1] (numeric) = 0.7406068829041188 absolute error = 3.05311331771918e-14 relative error = 4.122447938570293e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.162 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.162 Order of pole (three term test) = 3.005e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.162999999999982 y[1] (closed_form) = 0.7393338158718931 y[1] (numeric) = 0.7393338158718623 absolute error = 3.075317778211684e-14 relative error = 4.159579491957872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.163 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.163 Order of pole (three term test) = 3.083e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.163999999999982 y[1] (closed_form) = 0.7380640285306257 y[1] (numeric) = 0.7380640285305948 absolute error = 3.086420008457935e-14 relative error = 4.181778123779494e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.164 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.164 Order of pole (three term test) = 3.164e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.164999999999982 y[1] (closed_form) = 0.7367975096244402 y[1] (numeric) = 0.7367975096244092 absolute error = 3.108624468950438e-14 relative error = 4.219102844871128e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.165 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.165 Order of pole (three term test) = 3.247e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.165999999999982 y[1] (closed_form) = 0.7355342479456757 y[1] (numeric) = 0.7355342479456445 absolute error = 3.11972669919669e-14 relative error = 4.241443152252923e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.166 Order of pole (three term test) = 3.331e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.166999999999982 y[1] (closed_form) = 0.7342742323346698 y[1] (numeric) = 0.7342742323346385 absolute error = 3.130828929442941e-14 relative error = 4.263841479889985e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.167 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.167 Order of pole (three term test) = 3.418e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.167999999999982 y[1] (closed_form) = 0.7330174516795125 y[1] (numeric) = 0.7330174516794811 absolute error = 3.141931159689193e-14 relative error = 4.286297894395695e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.168 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.168 Order of pole (three term test) = 3.507e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.168999999999982 y[1] (closed_form) = 0.7317638949158006 y[1] (numeric) = 0.7317638949157691 absolute error = 3.153033389935445e-14 relative error = 4.308812462383435e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.169 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.169 Order of pole (three term test) = 3.598e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.169999999999981 y[1] (closed_form) = 0.7305135510263946 y[1] (numeric) = 0.730513551026363 absolute error = 3.164135620181696e-14 relative error = 4.331385250466587e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.17 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.17 Order of pole (three term test) = 3.692e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.170999999999981 y[1] (closed_form) = 0.7292664090411765 y[1] (numeric) = 0.7292664090411446 absolute error = 3.186340080674199e-14 relative error = 4.369240158563631e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.171 Order of pole (three term test) = 3.787e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.171999999999981 y[1] (closed_form) = 0.7280224580368088 y[1] (numeric) = 0.7280224580367768 absolute error = 3.197442310920451e-14 relative error = 4.391955599203216e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.172 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.172 Order of pole (three term test) = 7.771e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.172999999999981 y[1] (closed_form) = 0.7267816871364962 y[1] (numeric) = 0.7267816871364641 absolute error = 3.208544541166702e-14 relative error = 4.414729481982819e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.173 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.173 Order of pole (three term test) = 7.973e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.173999999999981 y[1] (closed_form) = 0.7255440855097471 y[1] (numeric) = 0.7255440855097148 absolute error = 3.230749001659206e-14 relative error = 4.4528638110107e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.174 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.174 Order of pole (three term test) = 4.09e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.174999999999981 y[1] (closed_form) = 0.7243096423721376 y[1] (numeric) = 0.7243096423721052 absolute error = 3.241851231905457e-14 relative error = 4.475780857049326e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.175 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.175 Order of pole (three term test) = 8.391e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.175999999999981 y[1] (closed_form) = 0.7230783469850761 y[1] (numeric) = 0.7230783469850436 absolute error = 3.252953462151709e-14 relative error = 4.498756567272575e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.176 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.176 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.176999999999981 y[1] (closed_form) = 0.7218501886555705 y[1] (numeric) = 0.7218501886555378 absolute error = 3.26405569239796e-14 relative error = 4.521791008293826e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.177 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.177 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.177999999999981 y[1] (closed_form) = 0.7206251567359954 y[1] (numeric) = 0.7206251567359626 absolute error = 3.275157922644212e-14 relative error = 4.54488424672646e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.178 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.178 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.178999999999981 y[1] (closed_form) = 0.7194032406238615 y[1] (numeric) = 0.7194032406238287 absolute error = 3.286260152890463e-14 relative error = 4.568036349183862e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.179 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.179 Order of pole (three term test) = 4.646e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.17999999999998 y[1] (closed_form) = 0.7181844297615866 y[1] (numeric) = 0.7181844297615536 absolute error = 3.297362383136715e-14 relative error = 4.59124738227941e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.18 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.18 Order of pole (three term test) = 7.148e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18099999999998 y[1] (closed_form) = 0.716968713636267 y[1] (numeric) = 0.7169687136362338 absolute error = 3.319566843629218e-14 relative error = 4.630002370386977e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.181 Order of pole (three term test) = 2.444e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18199999999998 y[1] (closed_form) = 0.7157560817794509 y[1] (numeric) = 0.7157560817794176 absolute error = 3.33066907387547e-14 relative error = 4.653357699169035e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.182 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.182 Order of pole (three term test) = 2.507e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18299999999998 y[1] (closed_form) = 0.7145465237669133 y[1] (numeric) = 0.7145465237668799 absolute error = 3.341771304121721e-14 relative error = 4.676772180633846e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.183 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.183 Order of pole (three term test) = 2.571e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18399999999998 y[1] (closed_form) = 0.7133400292184316 y[1] (numeric) = 0.7133400292183982 absolute error = 3.341771304121721e-14 relative error = 4.684682153310702e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.184 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.184 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18499999999998 y[1] (closed_form) = 0.7121365877975638 y[1] (numeric) = 0.7121365877975301 absolute error = 3.375077994860476e-14 relative error = 4.73936889733279e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.185 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.185 Order of pole (three term test) = 2.705e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18599999999998 y[1] (closed_form) = 0.7109361892114254 y[1] (numeric) = 0.7109361892113916 absolute error = 3.386180225106727e-14 relative error = 4.76298755991406e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.186 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.186 Order of pole (three term test) = 2.774e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18699999999998 y[1] (closed_form) = 0.7097388232104712 y[1] (numeric) = 0.7097388232104371 absolute error = 3.408384685599231e-14 relative error = 4.802308362083897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.187 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.187 Order of pole (three term test) = 5.691e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.18799999999998 y[1] (closed_form) = 0.708544479588275 y[1] (numeric) = 0.708544479588241 absolute error = 3.408384685599231e-14 relative error = 4.810403275712194e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.188 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.188 Order of pole (three term test) = 5.836e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.188999999999979 y[1] (closed_form) = 0.7073531481813135 y[1] (numeric) = 0.7073531481812793 absolute error = 3.419486915845482e-14 relative error = 4.834200462155824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.189 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.189 Order of pole (three term test) = 2.993e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.189999999999979 y[1] (closed_form) = 0.7061648188687486 y[1] (numeric) = 0.7061648188687142 absolute error = 3.441691376337985e-14 relative error = 4.873779158032051e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.19 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.19 Order of pole (three term test) = 9.208e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.190999999999979 y[1] (closed_form) = 0.7049794815722135 y[1] (numeric) = 0.704979481572179 absolute error = 3.441691376337985e-14 relative error = 4.881973825199111e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.191 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.191 Order of pole (three term test) = 6.295e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.191999999999979 y[1] (closed_form) = 0.7037971262555989 y[1] (numeric) = 0.7037971262555642 absolute error = 3.463895836830488e-14 relative error = 4.921724894302141e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.192 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.192 Order of pole (three term test) = 9.683e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.192999999999979 y[1] (closed_form) = 0.7026177429248397 y[1] (numeric) = 0.7026177429248051 absolute error = 3.463895836830488e-14 relative error = 4.929986285872983e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.193 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.193 Order of pole (three term test) = 3.31e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.193999999999979 y[1] (closed_form) = 0.7014413216277053 y[1] (numeric) = 0.7014413216276706 absolute error = 3.47499806707674e-14 relative error = 4.95408234435484e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.194 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.194 Order of pole (three term test) = 6.788e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.194999999999979 y[1] (closed_form) = 0.7002678524535884 y[1] (numeric) = 0.7002678524535535 absolute error = 3.486100297322992e-14 relative error = 4.978238377084488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.195 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.195 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.195999999999979 y[1] (closed_form) = 0.6990973255332965 y[1] (numeric) = 0.6990973255332614 absolute error = 3.508304757815495e-14 relative error = 5.018335258455229e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.196 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.196 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.196999999999979 y[1] (closed_form) = 0.6979297310388446 y[1] (numeric) = 0.6979297310388095 absolute error = 3.508304757815495e-14 relative error = 5.026730631740681e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.197 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.197 Order of pole (three term test) = 3.66e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.197999999999978 y[1] (closed_form) = 0.6967650591832493 y[1] (numeric) = 0.6967650591832141 absolute error = 3.519406988061746e-14 relative error = 5.051066986893988e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.198 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.198 Order of pole (three term test) = 3.752e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.198999999999978 y[1] (closed_form) = 0.6956033002203228 y[1] (numeric) = 0.6956033002202875 absolute error = 3.530509218307998e-14 relative error = 5.075463582748611e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.199 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.199 Order of pole (three term test) = 3.848e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.199999999999978 y[1] (closed_form) = 0.6944444444444696 y[1] (numeric) = 0.6944444444444343 absolute error = 3.530509218307998e-14 relative error = 5.083933274363333e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.2 Order of pole (three term test) = 7.89e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.200999999999978 y[1] (closed_form) = 0.6932884821904841 y[1] (numeric) = 0.6932884821904486 absolute error = 3.552713678800501e-14 relative error = 5.124437763015334e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.201 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.201 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.201999999999978 y[1] (closed_form) = 0.692135403833348 y[1] (numeric) = 0.6921354038333124 absolute error = 3.563815909046752e-14 relative error = 5.149015480654196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.202 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.202 Order of pole (three term test) = 8.294e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.202999999999978 y[1] (closed_form) = 0.6909851997880311 y[1] (numeric) = 0.6909851997879953 absolute error = 3.574918139293004e-14 relative error = 5.1736537054479e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.203 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.203 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.203999999999978 y[1] (closed_form) = 0.6898378605092914 y[1] (numeric) = 0.6898378605092554 absolute error = 3.597122599785507e-14 relative error = 5.214446474610475e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.204 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.204 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.204999999999978 y[1] (closed_form) = 0.6886933764914771 y[1] (numeric) = 0.688693376491441 absolute error = 3.608224830031759e-14 relative error = 5.239232658826671e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.205 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.205 Order of pole (three term test) = 4.469e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.205999999999978 y[1] (closed_form) = 0.6875517382683303 y[1] (numeric) = 0.6875517382682941 absolute error = 3.61932706027801e-14 relative error = 5.264079572242312e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.206 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.206 Order of pole (three term test) = 4.582e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.206999999999977 y[1] (closed_form) = 0.6864129364127904 y[1] (numeric) = 0.6864129364127541 absolute error = 3.630429290524262e-14 relative error = 5.288987281470783e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.207 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.207 Order of pole (three term test) = 4.697e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.207999999999977 y[1] (closed_form) = 0.6852769615368004 y[1] (numeric) = 0.685276961536764 absolute error = 3.641531520770513e-14 relative error = 5.313955853125463e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.208 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.208 Order of pole (three term test) = 9.631e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.208999999999977 y[1] (closed_form) = 0.6841438042911125 y[1] (numeric) = 0.684143804291076 absolute error = 3.652633751016765e-14 relative error = 5.338985353819735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.209 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.209 Order of pole (three term test) = 2.468e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.209999999999977 y[1] (closed_form) = 0.6830134553650966 y[1] (numeric) = 0.6830134553650599 absolute error = 3.674838211509268e-14 relative error = 5.380330625470515e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.21 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.21 Order of pole (three term test) = 5.06e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.210999999999977 y[1] (closed_form) = 0.6818859054865481 y[1] (numeric) = 0.6818859054865113 absolute error = 3.68594044175552e-14 relative error = 5.40550906258354e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.211 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.211999999999977 y[1] (closed_form) = 0.6807611454214988 y[1] (numeric) = 0.6807611454214619 absolute error = 3.68594044175552e-14 relative error = 5.414440096273914e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.212 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.212 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.212999999999977 y[1] (closed_form) = 0.6796391659740271 y[1] (numeric) = 0.6796391659739901 absolute error = 3.697042672001771e-14 relative error = 5.439713979260366e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.213 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.213 Order of pole (three term test) = 2.725e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.213999999999977 y[1] (closed_form) = 0.6785199579860703 y[1] (numeric) = 0.6785199579860332 absolute error = 3.719247132494274e-14 relative error = 5.481411546881321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.214 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.214 Order of pole (three term test) = 8.38e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.214999999999977 y[1] (closed_form) = 0.6774035123372376 y[1] (numeric) = 0.6774035123372003 absolute error = 3.730349362740526e-14 relative error = 5.50683498801142e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.215 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.215 Order of pole (three term test) = 2.863e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.215999999999976 y[1] (closed_form) = 0.6762898199446246 y[1] (numeric) = 0.6762898199445871 absolute error = 3.741451592986778e-14 relative error = 5.532319846679242e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.216 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.216 Order of pole (three term test) = 8.805e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.216999999999976 y[1] (closed_form) = 0.6751788717626279 y[1] (numeric) = 0.6751788717625905 absolute error = 3.741451592986778e-14 relative error = 5.541422798404979e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.217 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.217 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.217999999999976 y[1] (closed_form) = 0.6740706587827625 y[1] (numeric) = 0.674070658782725 absolute error = 3.752553823233029e-14 relative error = 5.56700365805774e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.218 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.218 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.218999999999976 y[1] (closed_form) = 0.6729651720334782 y[1] (numeric) = 0.6729651720334404 absolute error = 3.774758283725532e-14 relative error = 5.609143594042856e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.219 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.219 Order of pole (three term test) = 6.32e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.219999999999976 y[1] (closed_form) = 0.6718624025799781 y[1] (numeric) = 0.6718624025799402 absolute error = 3.785860513971784e-14 relative error = 5.634874788995381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.22 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.22 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.220999999999976 y[1] (closed_form) = 0.6707623415240388 y[1] (numeric) = 0.6707623415240008 absolute error = 3.796962744218035e-14 relative error = 5.660667734552536e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.221 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.221 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.221999999999976 y[1] (closed_form) = 0.6696649800038302 y[1] (numeric) = 0.6696649800037922 absolute error = 3.808064974464287e-14 relative error = 5.686522497327703e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.222 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.222 Order of pole (three term test) = 3.402e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.222999999999976 y[1] (closed_form) = 0.6685703091937375 y[1] (numeric) = 0.6685703091936993 absolute error = 3.819167204710538e-14 relative error = 5.712439143934262e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.223 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.223 Order of pole (three term test) = 3.486e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.223999999999976 y[1] (closed_form) = 0.6674783203041832 y[1] (numeric) = 0.6674783203041449 absolute error = 3.83026943495679e-14 relative error = 5.738417740985595e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.224 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.224 Order of pole (three term test) = 3.573e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.224999999999975 y[1] (closed_form) = 0.6663890045814511 y[1] (numeric) = 0.6663890045814127 absolute error = 3.841371665203042e-14 relative error = 5.764458355095083e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.225 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.225 Order of pole (three term test) = 3.662e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.225999999999975 y[1] (closed_form) = 0.6653023533075109 y[1] (numeric) = 0.6653023533074723 absolute error = 3.852473895449293e-14 relative error = 5.790561052876109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.226 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.226 Order of pole (three term test) = 3.752e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.226999999999975 y[1] (closed_form) = 0.6642183577998433 y[1] (numeric) = 0.6642183577998046 absolute error = 3.863576125695545e-14 relative error = 5.816725900942054e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.227 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.227 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.227999999999975 y[1] (closed_form) = 0.6631370094112673 y[1] (numeric) = 0.6631370094112284 absolute error = 3.885780586188048e-14 relative error = 5.85969495148196e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.228 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.228 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.228999999999975 y[1] (closed_form) = 0.6620582995297669 y[1] (numeric) = 0.6620582995297279 absolute error = 3.896882816434299e-14 relative error = 5.8860115781376e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.229 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.229 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.229999999999975 y[1] (closed_form) = 0.6609822195783204 y[1] (numeric) = 0.6609822195782812 absolute error = 3.919087276926803e-14 relative error = 5.929187141262317e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.23 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.23 Order of pole (three term test) = 4.137e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.230999999999975 y[1] (closed_form) = 0.6599087610147291 y[1] (numeric) = 0.6599087610146899 absolute error = 3.919087276926803e-14 relative error = 5.938832015050834e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.231 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.231 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.231999999999975 y[1] (closed_form) = 0.6588379153314489 y[1] (numeric) = 0.6588379153314096 absolute error = 3.930189507173054e-14 relative error = 5.965335958535189e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.232 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.232 Order of pole (three term test) = 8.688e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.232999999999975 y[1] (closed_form) = 0.6577696740554205 y[1] (numeric) = 0.6577696740553811 absolute error = 3.941291737419306e-14 relative error = 5.991902474189212e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.233 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.233 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.233999999999974 y[1] (closed_form) = 0.6567040287479027 y[1] (numeric) = 0.6567040287478632 absolute error = 3.952393967665557e-14 relative error = 6.018531628626285e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.234 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.234 Order of pole (three term test) = 9.122e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.234999999999974 y[1] (closed_form) = 0.6556409710043053 y[1] (numeric) = 0.6556409710042655 absolute error = 3.97459842815806e-14 relative error = 6.062156887587126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.235 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.235 Order of pole (three term test) = 2.336e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.235999999999974 y[1] (closed_form) = 0.6545804924540234 y[1] (numeric) = 0.6545804924539835 absolute error = 3.985700658404312e-14 relative error = 6.08893895304138e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.236 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.236 Order of pole (three term test) = 7.182e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.236999999999974 y[1] (closed_form) = 0.6535225847602728 y[1] (numeric) = 0.6535225847602328 absolute error = 3.996802888650564e-14 relative error = 6.115783879323288e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.237 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.237 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.237999999999974 y[1] (closed_form) = 0.652467239619926 y[1] (numeric) = 0.6524672396198861 absolute error = 3.996802888650564e-14 relative error = 6.125675966472698e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.238 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.238 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.238999999999974 y[1] (closed_form) = 0.6514144487633496 y[1] (numeric) = 0.6514144487633096 absolute error = 4.007905118896815e-14 relative error = 6.152619314025739e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.239 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.239 Order of pole (three term test) = 2.574e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.239999999999974 y[1] (closed_form) = 0.6503642039542419 y[1] (numeric) = 0.6503642039542016 absolute error = 4.030109579389318e-14 relative error = 6.196696489268754e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.24 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.24 Order of pole (three term test) = 2.638e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.240999999999974 y[1] (closed_form) = 0.6493164969894716 y[1] (numeric) = 0.6493164969894312 absolute error = 4.04121180963557e-14 relative error = 6.223793524995094e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.241 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.241 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.241999999999974 y[1] (closed_form) = 0.6482713196989185 y[1] (numeric) = 0.648271319698878 absolute error = 4.052314039881821e-14 relative error = 6.250953754615996e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.242 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.242 Order of pole (three term test) = 5.536e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.242999999999973 y[1] (closed_form) = 0.6472286639453134 y[1] (numeric) = 0.6472286639452728 absolute error = 4.063416270128073e-14 relative error = 6.278177244744842e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.243 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.243 Order of pole (three term test) = 5.672e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.243999999999973 y[1] (closed_form) = 0.6461885216240804 y[1] (numeric) = 0.6461885216240395 absolute error = 4.085620730620576e-14 relative error = 6.322645162981373e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.244 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.244 Order of pole (three term test) = 8.715e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.244999999999973 y[1] (closed_form) = 0.6451508846631784 y[1] (numeric) = 0.6451508846631373 absolute error = 4.107825191113079e-14 relative error = 6.367231741854776e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.245 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.245 Order of pole (three term test) = 5.952e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.245999999999973 y[1] (closed_form) = 0.6441157450229454 y[1] (numeric) = 0.6441157450229043 absolute error = 4.118927421359331e-14 relative error = 6.394700724498827e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.246 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.246 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.246999999999973 y[1] (closed_form) = 0.6430830946959427 y[1] (numeric) = 0.6430830946959015 absolute error = 4.118927421359331e-14 relative error = 6.404969210560275e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.247 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.247 Order of pole (three term test) = 6.246e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.247999999999973 y[1] (closed_form) = 0.6420529257067997 y[1] (numeric) = 0.6420529257067584 absolute error = 4.130029651605582e-14 relative error = 6.432537702494022e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.248 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.248 Order of pole (three term test) = 3.199e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.248999999999973 y[1] (closed_form) = 0.6410252301120599 y[1] (numeric) = 0.6410252301120185 absolute error = 4.141131881851834e-14 relative error = 6.460169876820461e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.249 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.249 Order of pole (three term test) = 6.553e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.249999999999973 y[1] (closed_form) = 0.640000000000028 y[1] (numeric) = 0.6399999999999865 absolute error = 4.152234112098085e-14 relative error = 6.487865800152975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.25 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.25 Order of pole (three term test) = 6.712e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.250999999999973 y[1] (closed_form) = 0.6389772274906175 y[1] (numeric) = 0.6389772274905758 absolute error = 4.163336342344337e-14 relative error = 6.515625539104944e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.251 Order of pole (three term test) = 6.875e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.251999999999972 y[1] (closed_form) = 0.6379569047351994 y[1] (numeric) = 0.6379569047351576 absolute error = 4.174438572590589e-14 relative error = 6.54344916028975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.252 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.252 Order of pole (three term test) = 3.521e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.252999999999972 y[1] (closed_form) = 0.6369390239164515 y[1] (numeric) = 0.6369390239164097 absolute error = 4.18554080283684e-14 relative error = 6.571336730320775e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.253 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.253 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.253999999999972 y[1] (closed_form) = 0.6359235772482088 y[1] (numeric) = 0.6359235772481668 absolute error = 4.196643033083092e-14 relative error = 6.599288315811399e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.254 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.254 Order of pole (three term test) = 7.388e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.254999999999972 y[1] (closed_form) = 0.6349105569753143 y[1] (numeric) = 0.6349105569752722 absolute error = 4.207745263329343e-14 relative error = 6.627303983375005e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.255 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.255 Order of pole (three term test) = 3.783e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.255999999999972 y[1] (closed_form) = 0.6338999553734713 y[1] (numeric) = 0.6338999553734291 absolute error = 4.218847493575595e-14 relative error = 6.655383799624973e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.256 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.256 Order of pole (three term test) = 3.875e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.256999999999972 y[1] (closed_form) = 0.6328917647490961 y[1] (numeric) = 0.6328917647490538 absolute error = 4.229949723821846e-14 relative error = 6.683527831174687e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.257 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.257 Order of pole (three term test) = 7.937e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.257999999999972 y[1] (closed_form) = 0.6318859774391713 y[1] (numeric) = 0.6318859774391289 absolute error = 4.241051954068098e-14 relative error = 6.711736144637525e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.258 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.258 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.258999999999972 y[1] (closed_form) = 0.6308825858111005 y[1] (numeric) = 0.6308825858110578 absolute error = 4.263256414560601e-14 relative error = 6.757606740847828e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.259 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.259 Order of pole (three term test) = 4.162e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.259999999999972 y[1] (closed_form) = 0.6298815822625631 y[1] (numeric) = 0.6298815822625203 absolute error = 4.274358644806853e-14 relative error = 6.785971784495053e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.26 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.26 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.260999999999971 y[1] (closed_form) = 0.6288829592213707 y[1] (numeric) = 0.6288829592213279 absolute error = 4.285460875053104e-14 relative error = 6.814401332100009e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.261 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.261 Order of pole (three term test) = 1.31e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.261999999999971 y[1] (closed_form) = 0.627886709145324 y[1] (numeric) = 0.627886709145281 absolute error = 4.296563105299356e-14 relative error = 6.842895450276077e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.262 Order of pole (three term test) = 4.47e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.262999999999971 y[1] (closed_form) = 0.6268928245220697 y[1] (numeric) = 0.6268928245220267 absolute error = 4.307665335545607e-14 relative error = 6.871454205636639e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.263 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.263 Order of pole (three term test) = 9.156e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.263999999999971 y[1] (closed_form) = 0.6259012978689599 y[1] (numeric) = 0.6259012978689166 absolute error = 4.329869796038111e-14 relative error = 6.917815653650589e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.264 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.264 Order of pole (three term test) = 7.032e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.264999999999971 y[1] (closed_form) = 0.6249121217329099 y[1] (numeric) = 0.6249121217328666 absolute error = 4.329869796038111e-14 relative error = 6.928765894364769e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.265 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.265 Order of pole (three term test) = 2.4e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.265999999999971 y[1] (closed_form) = 0.6239252886902598 y[1] (numeric) = 0.6239252886902162 absolute error = 4.352074256530614e-14 relative error = 6.975313127099659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.266 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.266 Order of pole (three term test) = 2.458e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.266999999999971 y[1] (closed_form) = 0.6229407913466336 y[1] (numeric) = 0.62294079134659 absolute error = 4.363176486776865e-14 relative error = 7.004159219281224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.267 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.267 Order of pole (three term test) = 2.517e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.267999999999971 y[1] (closed_form) = 0.6219586223368019 y[1] (numeric) = 0.6219586223367582 absolute error = 4.363176486776865e-14 relative error = 7.015219871675203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.268 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.268 Order of pole (three term test) = 7.731e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.268999999999971 y[1] (closed_form) = 0.6209787743245436 y[1] (numeric) = 0.6209787743244998 absolute error = 4.385380947269368e-14 relative error = 7.062046447625319e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.269 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.269 Order of pole (three term test) = 2.639e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.26999999999997 y[1] (closed_form) = 0.6200012400025088 y[1] (numeric) = 0.6200012400024649 absolute error = 4.385380947269368e-14 relative error = 7.073180929850436e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.27 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 Order of pole (three term test) = 5.403e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27099999999997 y[1] (closed_form) = 0.619026012092083 y[1] (numeric) = 0.619026012092039 absolute error = 4.39648317751562e-14 relative error = 7.10225918076868e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.271 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.271 Order of pole (three term test) = 5.532e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27199999999997 y[1] (closed_form) = 0.618053083343251 y[1] (numeric) = 0.618053083343207 absolute error = 4.407585407761871e-14 relative error = 7.131402668391851e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.272 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.272 Order of pole (three term test) = 5.665e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27299999999997 y[1] (closed_form) = 0.6170824465344631 y[1] (numeric) = 0.6170824465344188 absolute error = 4.429789868254375e-14 relative error = 7.178602945412057e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.273 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.273 Order of pole (three term test) = 2.9e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27399999999997 y[1] (closed_form) = 0.6161140944724998 y[1] (numeric) = 0.6161140944724554 absolute error = 4.440892098500626e-14 relative error = 7.207905383665663e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.274 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.274 Order of pole (three term test) = 5.938e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27499999999997 y[1] (closed_form) = 0.6151480199923397 y[1] (numeric) = 0.6151480199922952 absolute error = 4.451994328746878e-14 relative error = 7.237273280668801e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.275 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.275 Order of pole (three term test) = 3.04e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27599999999997 y[1] (closed_form) = 0.6141842159570263 y[1] (numeric) = 0.6141842159569817 absolute error = 4.463096558993129e-14 relative error = 7.266706703034854e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.276 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.276 Order of pole (three term test) = 3.112e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27699999999997 y[1] (closed_form) = 0.6132226752575366 y[1] (numeric) = 0.6132226752574919 absolute error = 4.474198789239381e-14 relative error = 7.296205717377201e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.277 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.277 Order of pole (three term test) = 3.186e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.27799999999997 y[1] (closed_form) = 0.6122633908126496 y[1] (numeric) = 0.6122633908126047 absolute error = 4.485301019485632e-14 relative error = 7.325770390309224e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.278 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.278 Order of pole (three term test) = 3.262e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.278999999999969 y[1] (closed_form) = 0.6113063555688162 y[1] (numeric) = 0.6113063555687711 absolute error = 4.507505479978136e-14 relative error = 7.373562271872561e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.279 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.279 Order of pole (three term test) = 6.678e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.279999999999969 y[1] (closed_form) = 0.6103515625000292 y[1] (numeric) = 0.6103515624999841 absolute error = 4.507505479978136e-14 relative error = 7.385096978395824e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.28 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.28 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.280999999999969 y[1] (closed_form) = 0.6093990046076951 y[1] (numeric) = 0.60939900460765 absolute error = 4.518607710224387e-14 relative error = 7.414859026777165e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.281 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.281 Order of pole (three term test) = 3.499e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.281999999999969 y[1] (closed_form) = 0.608448674920505 y[1] (numeric) = 0.6084486749204597 absolute error = 4.529709940470639e-14 relative error = 7.444687000201708e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.282 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.282 Order of pole (three term test) = 7.165e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.282999999999969 y[1] (closed_form) = 0.6075005664943075 y[1] (numeric) = 0.6075005664942622 absolute error = 4.529709940470639e-14 relative error = 7.456305706199014e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.283 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.283 Order of pole (three term test) = 3.667e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.283999999999969 y[1] (closed_form) = 0.6065546724119819 y[1] (numeric) = 0.6065546724119364 absolute error = 4.551914400963142e-14 relative error = 7.504540988633925e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.284 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.284 Order of pole (three term test) = 3.754e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.284999999999969 y[1] (closed_form) = 0.6056109857833115 y[1] (numeric) = 0.6056109857832659 absolute error = 4.563016631209393e-14 relative error = 7.534567136868364e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.285 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.285 Order of pole (three term test) = 7.685e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.285999999999969 y[1] (closed_form) = 0.6046694997448588 y[1] (numeric) = 0.6046694997448132 absolute error = 4.563016631209393e-14 relative error = 7.546298652627203e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.286 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.286 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.286999999999969 y[1] (closed_form) = 0.6037302074598406 y[1] (numeric) = 0.6037302074597949 absolute error = 4.574118861455645e-14 relative error = 7.576428684430056e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.287 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.287 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.287999999999969 y[1] (closed_form) = 0.6027931021180033 y[1] (numeric) = 0.6027931021179574 absolute error = 4.585221091701897e-14 relative error = 7.606625018751939e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.288 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.288 Order of pole (three term test) = 4.121e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.288999999999968 y[1] (closed_form) = 0.6018581769355 y[1] (numeric) = 0.6018581769354541 absolute error = 4.596323321948148e-14 relative error = 7.636887722206234e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.289 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.289 Order of pole (three term test) = 4.218e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.289999999999968 y[1] (closed_form) = 0.6009254251547679 y[1] (numeric) = 0.6009254251547217 absolute error = 4.618527782440651e-14 relative error = 7.685692082759109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.29 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.29 Order of pole (three term test) = 4.317e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.290999999999968 y[1] (closed_form) = 0.5999948400444052 y[1] (numeric) = 0.599994840044359 absolute error = 4.618527782440651e-14 relative error = 7.697612502965588e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.291 Order of pole (three term test) = 4.419e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.291999999999968 y[1] (closed_form) = 0.599066414899051 y[1] (numeric) = 0.5990664148990047 absolute error = 4.629630012686903e-14 relative error = 7.728074713497409e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.292 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.292 Order of pole (three term test) = 4.523e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.292999999999968 y[1] (closed_form) = 0.5981401430392634 y[1] (numeric) = 0.598140143039217 absolute error = 4.640732242933154e-14 relative error = 7.758603559615166e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.293 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.293 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.293999999999968 y[1] (closed_form) = 0.5972160178114002 y[1] (numeric) = 0.5972160178113537 absolute error = 4.651834473179406e-14 relative error = 7.789199107932245e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.294 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.294 Order of pole (three term test) = 2.369e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.294999999999968 y[1] (closed_form) = 0.5962940325874986 y[1] (numeric) = 0.5962940325874519 absolute error = 4.662936703425657e-14 relative error = 7.819861425062024e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.295 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.295 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.295999999999968 y[1] (closed_form) = 0.595374180765157 y[1] (numeric) = 0.5953741807651103 absolute error = 4.674038933671909e-14 relative error = 7.850590577617884e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.296 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.296 Order of pole (three term test) = 4.962e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.296999999999968 y[1] (closed_form) = 0.5944564557674166 y[1] (numeric) = 0.5944564557673697 absolute error = 4.685141163918161e-14 relative error = 7.88138663221321e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.297 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.297 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.297999999999967 y[1] (closed_form) = 0.5935408510426436 y[1] (numeric) = 0.5935408510425967 absolute error = 4.696243394164412e-14 relative error = 7.912249655461381e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.298 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.298 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.298999999999967 y[1] (closed_form) = 0.5926273600644129 y[1] (numeric) = 0.5926273600643658 absolute error = 4.707345624410664e-14 relative error = 7.943179713975779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.299 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.299 Order of pole (three term test) = 5.319e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.299999999999967 y[1] (closed_form) = 0.5917159763313908 y[1] (numeric) = 0.5917159763313437 absolute error = 4.718447854656915e-14 relative error = 7.974176874369785e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.3 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.3 Order of pole (three term test) = 2.721e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.300999999999967 y[1] (closed_form) = 0.5908066933672205 y[1] (numeric) = 0.5908066933671732 absolute error = 4.729550084903167e-14 relative error = 8.005241203256779e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.301 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.301 Order of pole (three term test) = 2.785e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.301999999999967 y[1] (closed_form) = 0.5898995047204058 y[1] (numeric) = 0.5898995047203585 absolute error = 4.729550084903167e-14 relative error = 8.017552222127782e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.302 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.302 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.302999999999967 y[1] (closed_form) = 0.5889944039641979 y[1] (numeric) = 0.5889944039641505 absolute error = 4.740652315149418e-14 relative error = 8.048722166531109e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.303 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.303 Order of pole (three term test) = 2.916e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.303999999999967 y[1] (closed_form) = 0.5880913846964807 y[1] (numeric) = 0.5880913846964332 absolute error = 4.75175454539567e-14 relative error = 8.079959457063111e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.304 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.304 Order of pole (three term test) = 5.968e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.304999999999967 y[1] (closed_form) = 0.5871904405396581 y[1] (numeric) = 0.5871904405396103 absolute error = 4.773959005888173e-14 relative error = 8.130171536002291e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.305 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.305 Order of pole (three term test) = 6.107e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.305999999999967 y[1] (closed_form) = 0.5862915651405407 y[1] (numeric) = 0.5862915651404929 absolute error = 4.785061236134425e-14 relative error = 8.161572706554956e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.306 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.306 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.306999999999966 y[1] (closed_form) = 0.5853947521702347 y[1] (numeric) = 0.5853947521701869 absolute error = 4.785061236134425e-14 relative error = 8.174076071564975e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.307 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.307 Order of pole (three term test) = 3.197e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.307999999999966 y[1] (closed_form) = 0.5844999953240301 y[1] (numeric) = 0.5844999953239821 absolute error = 4.796163466380676e-14 relative error = 8.205583412745488e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.308 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.308 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.308999999999966 y[1] (closed_form) = 0.5836072883212896 y[1] (numeric) = 0.5836072883212414 absolute error = 4.818367926873179e-14 relative error = 8.256181893706156e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.309 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.309 Order of pole (three term test) = 3.347e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.309999999999966 y[1] (closed_form) = 0.5827166249053387 y[1] (numeric) = 0.5827166249052904 absolute error = 4.829470157119431e-14 relative error = 8.287853736632226e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.31 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.31 Order of pole (three term test) = 6.85e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.310999999999966 y[1] (closed_form) = 0.5818279988433561 y[1] (numeric) = 0.5818279988433077 absolute error = 4.840572387365683e-14 relative error = 8.319593414185102e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.311 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.311 Order of pole (three term test) = 3.504e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.311999999999966 y[1] (closed_form) = 0.5809414039262647 y[1] (numeric) = 0.5809414039262161 absolute error = 4.862776847858186e-14 relative error = 8.370511750399164e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.312 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.312 Order of pole (three term test) = 7.17e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.312999999999966 y[1] (closed_form) = 0.5800568339686225 y[1] (numeric) = 0.5800568339685739 absolute error = 4.862776847858186e-14 relative error = 8.383276539624791e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.313 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.313 Order of pole (three term test) = 3.668e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.313999999999966 y[1] (closed_form) = 0.5791742828085159 y[1] (numeric) = 0.5791742828084672 absolute error = 4.873879078104437e-14 relative error = 8.415220120738368e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.314 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.314 Order of pole (three term test) = 7.506e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.314999999999966 y[1] (closed_form) = 0.5782937443074513 y[1] (numeric) = 0.5782937443074024 absolute error = 4.884981308350689e-14 relative error = 8.447231802932276e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.315 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.315 Order of pole (three term test) = 7.679e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.315999999999965 y[1] (closed_form) = 0.5774152123502488 y[1] (numeric) = 0.5774152123501999 absolute error = 4.89608353859694e-14 relative error = 8.479311652819897e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.316 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.316 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.316999999999965 y[1] (closed_form) = 0.5765386808449363 y[1] (numeric) = 0.5765386808448872 absolute error = 4.907185768843192e-14 relative error = 8.511459737014609e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.317 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.317 Order of pole (three term test) = 1.206e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.317999999999965 y[1] (closed_form) = 0.5756641437226432 y[1] (numeric) = 0.575664143722594 absolute error = 4.918287999089443e-14 relative error = 8.543676122129798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.318 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.318 Order of pole (three term test) = 4.111e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.318999999999965 y[1] (closed_form) = 0.574791594937496 y[1] (numeric) = 0.5747915949374467 absolute error = 4.929390229335695e-14 relative error = 8.575960874778844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.319 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.319 Order of pole (three term test) = 4.206e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.319999999999965 y[1] (closed_form) = 0.5739210284665135 y[1] (numeric) = 0.5739210284664641 absolute error = 4.940492459581947e-14 relative error = 8.608314061575127e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.32 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.32 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.320999999999965 y[1] (closed_form) = 0.5730524383095028 y[1] (numeric) = 0.5730524383094534 absolute error = 4.940492459581947e-14 relative error = 8.621361902160883e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.321 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.321 Order of pole (three term test) = 4.401e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.321999999999965 y[1] (closed_form) = 0.5721858184889564 y[1] (numeric) = 0.5721858184889068 absolute error = 4.96269692007445e-14 relative error = 8.673226004062932e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.322 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.322 Order of pole (three term test) = 9.005e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.322999999999965 y[1] (closed_form) = 0.5713211630499486 y[1] (numeric) = 0.5713211630498989 absolute error = 4.973799150320701e-14 relative error = 8.705784892981217e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.323 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.323 Order of pole (three term test) = 4.606e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.323999999999965 y[1] (closed_form) = 0.5704584660600337 y[1] (numeric) = 0.5704584660599838 absolute error = 4.984901380566953e-14 relative error = 8.738412482500265e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.324 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.324 Order of pole (three term test) = 2.356e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.324999999999964 y[1] (closed_form) = 0.5695977216091441 y[1] (numeric) = 0.5695977216090943 absolute error = 4.984901380566953e-14 relative error = 8.751617486257386e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.325 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.325 Order of pole (three term test) = 7.229e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.325999999999964 y[1] (closed_form) = 0.5687389238094894 y[1] (numeric) = 0.5687389238094395 absolute error = 4.996003610813204e-14 relative error = 8.784353244805724e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.326 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.326 Order of pole (three term test) = 2.465e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.326999999999964 y[1] (closed_form) = 0.5678820667954551 y[1] (numeric) = 0.5678820667954051 absolute error = 4.996003610813204e-14 relative error = 8.797607642385211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.327 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.327 Order of pole (three term test) = 5.042e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.327999999999964 y[1] (closed_form) = 0.5670271447235029 y[1] (numeric) = 0.5670271447234527 absolute error = 5.018208071305708e-14 relative error = 8.850031463225126e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.328 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.328 Order of pole (three term test) = 5.157e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.328999999999964 y[1] (closed_form) = 0.5661741517720709 y[1] (numeric) = 0.5661741517720206 absolute error = 5.029310301551959e-14 relative error = 8.882974056322953e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.329 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.329 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.329999999999964 y[1] (closed_form) = 0.5653230821414745 y[1] (numeric) = 0.5653230821414241 absolute error = 5.040412531798211e-14 relative error = 8.915985727497372e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.33 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.33 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.330999999999964 y[1] (closed_form) = 0.5644739300538082 y[1] (numeric) = 0.5644739300537577 absolute error = 5.051514762044462e-14 relative error = 8.949066543361762e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.331 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.331 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.331999999999964 y[1] (closed_form) = 0.5636266897528467 y[1] (numeric) = 0.5636266897527961 absolute error = 5.062616992290714e-14 relative error = 8.982216570529509e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.332 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.332 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.332999999999964 y[1] (closed_form) = 0.562781355503948 y[1] (numeric) = 0.5627813555038974 absolute error = 5.062616992290714e-14 relative error = 8.995708444813963e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.333 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.333 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.333999999999963 y[1] (closed_form) = 0.5619379215939565 y[1] (numeric) = 0.5619379215939058 absolute error = 5.073719222536965e-14 relative error = 9.028967484780497e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.334 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.334 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.334999999999963 y[1] (closed_form) = 0.5610963823311058 y[1] (numeric) = 0.561096382331055 absolute error = 5.084821452783217e-14 relative error = 9.062295913686069e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.335 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.335 Order of pole (three term test) = 3.019e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.335999999999963 y[1] (closed_form) = 0.5602567320449231 y[1] (numeric) = 0.5602567320448723 absolute error = 5.084821452783217e-14 relative error = 9.075877471786453e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.336 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.336 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.336999999999963 y[1] (closed_form) = 0.5594189650861339 y[1] (numeric) = 0.5594189650860829 absolute error = 5.095923683029469e-14 relative error = 9.109315202148801e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.337 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.337 Order of pole (three term test) = 3.158e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.337999999999963 y[1] (closed_form) = 0.5585830758265662 y[1] (numeric) = 0.5585830758265152 absolute error = 5.095923683029469e-14 relative error = 9.122946798000905e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.338 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.338 Order of pole (three term test) = 3.23e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.338999999999963 y[1] (closed_form) = 0.5577490586590572 y[1] (numeric) = 0.557749058659006 absolute error = 5.118128143521972e-14 relative error = 9.176399429211048e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.339 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.339 Order of pole (three term test) = 3.303e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.339999999999963 y[1] (closed_form) = 0.5569169079973577 y[1] (numeric) = 0.5569169079973065 absolute error = 5.118128143521972e-14 relative error = 9.190110894507542e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.34 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.34 Order of pole (three term test) = 3.378e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.340999999999963 y[1] (closed_form) = 0.5560866182760401 y[1] (numeric) = 0.5560866182759888 absolute error = 5.129230373768223e-14 relative error = 9.223797525769781e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.341 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.341 Order of pole (three term test) = 6.908e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.341999999999963 y[1] (closed_form) = 0.5552581839504042 y[1] (numeric) = 0.5552581839503529 absolute error = 5.129230373768223e-14 relative error = 9.237559250862601e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.342 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.342 Order of pole (three term test) = 3.532e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.342999999999962 y[1] (closed_form) = 0.5544315994963853 y[1] (numeric) = 0.5544315994963339 absolute error = 5.140332604014475e-14 relative error = 9.271355760897586e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.343 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.343 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.343999999999962 y[1] (closed_form) = 0.5536068594104619 y[1] (numeric) = 0.5536068594104103 absolute error = 5.162537064506978e-14 relative error = 9.325276550952753e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.344 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.344 Order of pole (three term test) = 7.387e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.344999999999962 y[1] (closed_form) = 0.5527839582095638 y[1] (numeric) = 0.5527839582095122 absolute error = 5.162537064506978e-14 relative error = 9.339158613119211e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.345 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.345 Order of pole (three term test) = 3.777e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.345999999999962 y[1] (closed_form) = 0.5519628904309816 y[1] (numeric) = 0.5519628904309299 absolute error = 5.162537064506978e-14 relative error = 9.353051000359798e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.346 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.346 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.346999999999962 y[1] (closed_form) = 0.5511436506322756 y[1] (numeric) = 0.5511436506322238 absolute error = 5.173639294753229e-14 relative error = 9.387097699153383e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.347 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.347 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.347999999999962 y[1] (closed_form) = 0.5503262333911854 y[1] (numeric) = 0.5503262333911336 absolute error = 5.173639294753229e-14 relative error = 9.401040657052741e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.348 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.348 Order of pole (three term test) = 4.038e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.348999999999962 y[1] (closed_form) = 0.549510633305541 y[1] (numeric) = 0.5495106333054891 absolute error = 5.184741524999481e-14 relative error = 9.435197811935045e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.349 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.349 Order of pole (three term test) = 4.129e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.349999999999962 y[1] (closed_form) = 0.5486968449931725 y[1] (numeric) = 0.5486968449931205 absolute error = 5.195843755245733e-14 relative error = 9.46942524393481e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.35 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.35 Order of pole (three term test) = 4.222e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.350999999999962 y[1] (closed_form) = 0.5478848630918222 y[1] (numeric) = 0.5478848630917702 absolute error = 5.195843755245733e-14 relative error = 9.483459217917726e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.351 Order of pole (three term test) = 4.316e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.351999999999961 y[1] (closed_form) = 0.5470746822590558 y[1] (numeric) = 0.5470746822590037 absolute error = 5.206945985491984e-14 relative error = 9.517797394664197e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.352 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.352 Order of pole (three term test) = 4.413e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.352999999999961 y[1] (closed_form) = 0.5462662971721745 y[1] (numeric) = 0.5462662971721224 absolute error = 5.206945985491984e-14 relative error = 9.531882183554951e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.353 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.353 Order of pole (three term test) = 4.512e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.353999999999961 y[1] (closed_form) = 0.5454597025281278 y[1] (numeric) = 0.5454597025280756 absolute error = 5.218048215738236e-14 relative error = 9.566331282683813e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.354 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.354 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.354999999999961 y[1] (closed_form) = 0.5446548930434266 y[1] (numeric) = 0.5446548930433743 absolute error = 5.229150445984487e-14 relative error = 9.600850947588117e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.355 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.355 Order of pole (three term test) = 2.358e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.355999999999961 y[1] (closed_form) = 0.5438518634540562 y[1] (numeric) = 0.5438518634540038 absolute error = 5.240252676230739e-14 relative error = 9.63544124488125e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.356 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.356 Order of pole (three term test) = 2.411e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.356999999999961 y[1] (closed_form) = 0.5430506085153907 y[1] (numeric) = 0.5430506085153382 absolute error = 5.25135490647699e-14 relative error = 9.67010224117659e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.357 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.357 Order of pole (three term test) = 4.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.357999999999961 y[1] (closed_form) = 0.5422511230021071 y[1] (numeric) = 0.5422511230020545 absolute error = 5.262457136723242e-14 relative error = 9.704834003087519e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.358 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.358 Order of pole (three term test) = 5.04e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.358999999999961 y[1] (closed_form) = 0.5414534017081003 y[1] (numeric) = 0.5414534017080476 absolute error = 5.273559366969494e-14 relative error = 9.73963659722742e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.359 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.359 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.359999999999961 y[1] (closed_form) = 0.5406574394463982 y[1] (numeric) = 0.5406574394463454 absolute error = 5.284661597215745e-14 relative error = 9.774510090209674e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.36 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.36 Order of pole (three term test) = 2.634e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36099999999996 y[1] (closed_form) = 0.5398632310490774 y[1] (numeric) = 0.5398632310490246 absolute error = 5.284661597215745e-14 relative error = 9.788889654415697e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.361 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.361 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36199999999996 y[1] (closed_form) = 0.5390707713671795 y[1] (numeric) = 0.5390707713671267 absolute error = 5.284661597215745e-14 relative error = 9.803279787944915e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.362 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.362 Order of pole (three term test) = 5.505e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36299999999996 y[1] (closed_form) = 0.5382800552706275 y[1] (numeric) = 0.5382800552705745 absolute error = 5.295763827461997e-14 relative error = 9.838305869979672e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.363 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.363 Order of pole (three term test) = 2.814e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36399999999996 y[1] (closed_form) = 0.5374910776481425 y[1] (numeric) = 0.5374910776480895 absolute error = 5.306866057708248e-14 relative error = 9.873403072901388e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.364 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.364 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36499999999996 y[1] (closed_form) = 0.5367038334071615 y[1] (numeric) = 0.5367038334071085 absolute error = 5.306866057708248e-14 relative error = 9.887885510372872e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.365 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.365 Order of pole (three term test) = 2.94e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36599999999996 y[1] (closed_form) = 0.5359183174737554 y[1] (numeric) = 0.5359183174737022 absolute error = 5.3179682879545e-14 relative error = 9.923094834717844e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.366 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.366 Order of pole (three term test) = 3.006e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36699999999996 y[1] (closed_form) = 0.5351345247925464 y[1] (numeric) = 0.5351345247924932 absolute error = 5.3179682879545e-14 relative error = 9.937628842048823e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.367 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.367 Order of pole (three term test) = 3.072e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36799999999996 y[1] (closed_form) = 0.5343524503266277 y[1] (numeric) = 0.5343524503265744 absolute error = 5.329070518200751e-14 relative error = 9.972950465452735e-12 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 14 h = -0.001 Radius of convergence (given) for eq 1 = 1.368 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.368 Order of pole (three term test) = 6.281e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.36899999999996 y[1] (closed_form) = 0.5335720890574818 y[1] (numeric) = 0.5335720890574284 absolute error = 5.340172748447003e-14 relative error = 1.000834349840159e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.369 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.369 Order of pole (three term test) = 9.631e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.369999999999959 y[1] (closed_form) = 0.5327934359849003 y[1] (numeric) = 0.5327934359848467 absolute error = 5.351274978693255e-14 relative error = 1.004380800750877e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.37 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.37 Order of pole (three term test) = 3.281e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.370999999999959 y[1] (closed_form) = 0.5320164861269037 y[1] (numeric) = 0.5320164861268502 absolute error = 5.351274978693255e-14 relative error = 1.005847585222537e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.371 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.371 Order of pole (three term test) = 6.708e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.371999999999959 y[1] (closed_form) = 0.531241234519662 y[1] (numeric) = 0.5312412345196084 absolute error = 5.362377208939506e-14 relative error = 1.009405306007178e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.372 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.372 Order of pole (three term test) = 3.428e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.372999999999959 y[1] (closed_form) = 0.5304676762174151 y[1] (numeric) = 0.5304676762173614 absolute error = 5.373479439185758e-14 relative error = 1.012970192171221e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.373 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.373 Order of pole (three term test) = 3.504e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.373999999999959 y[1] (closed_form) = 0.5296958062923941 y[1] (numeric) = 0.5296958062923401 absolute error = 5.395683899678261e-14 relative error = 1.018638213778839e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.374 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.374 Order of pole (three term test) = 7.163e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.374999999999959 y[1] (closed_form) = 0.5289256198347424 y[1] (numeric) = 0.5289256198346884 absolute error = 5.395683899678261e-14 relative error = 1.02012148728286e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.375 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.375 Order of pole (three term test) = 3.66e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.375999999999959 y[1] (closed_form) = 0.5281571119524383 y[1] (numeric) = 0.5281571119523844 absolute error = 5.395683899678261e-14 relative error = 1.021605839923661e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.376 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.376 Order of pole (three term test) = 3.741e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.376999999999959 y[1] (closed_form) = 0.5273902777712171 y[1] (numeric) = 0.527390277771163 absolute error = 5.406786129924512e-14 relative error = 1.025196397774702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.377 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.377 Order of pole (three term test) = 7.647e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.377999999999959 y[1] (closed_form) = 0.5266251124344932 y[1] (numeric) = 0.526625112434439 absolute error = 5.417888360170764e-14 relative error = 1.028794152091388e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.378 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.378 Order of pole (three term test) = 3.908e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.378999999999958 y[1] (closed_form) = 0.5258616111032841 y[1] (numeric) = 0.5258616111032298 absolute error = 5.428990590417015e-14 relative error = 1.032399109535058e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.379 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.379 Order of pole (three term test) = 7.987e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.379999999999958 y[1] (closed_form) = 0.5250997689561333 y[1] (numeric) = 0.525099768956079 absolute error = 5.428990590417015e-14 relative error = 1.033896968038954e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.38 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.38 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.380999999999958 y[1] (closed_form) = 0.5243395811890346 y[1] (numeric) = 0.5243395811889802 absolute error = 5.440092820663267e-14 relative error = 1.037513286394835e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.381 Order of pole (three term test) = 4.171e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.381999999999958 y[1] (closed_form) = 0.5235810430153559 y[1] (numeric) = 0.5235810430153014 absolute error = 5.451195050909519e-14 relative error = 1.041136825641268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.382 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.382 Order of pole (three term test) = 4.263e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.382999999999958 y[1] (closed_form) = 0.5228241496657641 y[1] (numeric) = 0.5228241496657096 absolute error = 5.451195050909519e-14 relative error = 1.042644081072844e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.383 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.383 Order of pole (three term test) = 8.712e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.383999999999958 y[1] (closed_form) = 0.5220688963881503 y[1] (numeric) = 0.5220688963880956 absolute error = 5.473399511402022e-14 relative error = 1.048405593451143e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.384 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 Order of pole (three term test) = 4.452e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.384999999999958 y[1] (closed_form) = 0.5213152784475549 y[1] (numeric) = 0.5213152784475001 absolute error = 5.473399511402022e-14 relative error = 1.04992117777585e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.385 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.385 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.385999999999958 y[1] (closed_form) = 0.5205632911260935 y[1] (numeric) = 0.5205632911260386 absolute error = 5.484501741648273e-14 relative error = 1.053570590769872e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.386 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.386 Order of pole (three term test) = 2.324e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.386999999999958 y[1] (closed_form) = 0.5198129297228832 y[1] (numeric) = 0.5198129297228282 absolute error = 5.495603971894525e-14 relative error = 1.057227255740691e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.387 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.387 Order of pole (three term test) = 2.375e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.387999999999957 y[1] (closed_form) = 0.5190641895539688 y[1] (numeric) = 0.5190641895539138 absolute error = 5.506706202140776e-14 relative error = 1.060891179349645e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.388 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.388 Order of pole (three term test) = 4.854e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.388999999999957 y[1] (closed_form) = 0.5183170659522502 y[1] (numeric) = 0.5183170659521951 absolute error = 5.517808432387028e-14 relative error = 1.064562368258072e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.389 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.389 Order of pole (three term test) = 4.96e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.389999999999957 y[1] (closed_form) = 0.5175715542674092 y[1] (numeric) = 0.517571554267354 absolute error = 5.517808432387028e-14 relative error = 1.066095767221432e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.39 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.39 Order of pole (three term test) = 2.534e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.390999999999957 y[1] (closed_form) = 0.5168276498658375 y[1] (numeric) = 0.5168276498657822 absolute error = 5.52891066263328e-14 relative error = 1.069778419182588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.391 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.391 Order of pole (three term test) = 2.59e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.391999999999957 y[1] (closed_form) = 0.5160853481305643 y[1] (numeric) = 0.5160853481305089 absolute error = 5.540012892879531e-14 relative error = 1.073468354206786e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.392 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.392 Order of pole (three term test) = 5.292e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.392999999999957 y[1] (closed_form) = 0.5153446444611849 y[1] (numeric) = 0.5153446444611295 absolute error = 5.540012892879531e-14 relative error = 1.075011247797453e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.393 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.393 Order of pole (three term test) = 5.407e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.393999999999957 y[1] (closed_form) = 0.5146055342737897 y[1] (numeric) = 0.5146055342737341 absolute error = 5.562217353372034e-14 relative error = 1.080870100089659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.394 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.394 Order of pole (three term test) = 5.525e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.394999999999957 y[1] (closed_form) = 0.5138680130008926 y[1] (numeric) = 0.513868013000837 absolute error = 5.562217353372034e-14 relative error = 1.082421402509514e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.395 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.395 Order of pole (three term test) = 5.645e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.395999999999957 y[1] (closed_form) = 0.5131320760913611 y[1] (numeric) = 0.5131320760913055 absolute error = 5.562217353372034e-14 relative error = 1.08397381737284e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.396 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.396 Order of pole (three term test) = 2.884e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.396999999999956 y[1] (closed_form) = 0.512397719010346 y[1] (numeric) = 0.5123977190102902 absolute error = 5.584421813864537e-14 relative error = 1.089860787173368e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.397 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.397 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.397999999999956 y[1] (closed_form) = 0.5116649372392107 y[1] (numeric) = 0.5116649372391548 absolute error = 5.584421813864537e-14 relative error = 1.091421633070343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.398 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.398 Order of pole (three term test) = 3.01e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.398999999999956 y[1] (closed_form) = 0.510933726275463 y[1] (numeric) = 0.5109337262754071 absolute error = 5.584421813864537e-14 relative error = 1.092983595851681e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.399 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.399 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.399999999999956 y[1] (closed_form) = 0.5102040816326849 y[1] (numeric) = 0.510204081632629 absolute error = 5.595524044110789e-14 relative error = 1.096722712645646e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.4 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.4 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.400999999999956 y[1] (closed_form) = 0.5094759988404646 y[1] (numeric) = 0.5094759988404085 absolute error = 5.606626274357041e-14 relative error = 1.100469165793358e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.401 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.401 Order of pole (three term test) = 6.421e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.401999999999956 y[1] (closed_form) = 0.508749473444327 y[1] (numeric) = 0.5087494734442708 absolute error = 5.617728504603292e-14 relative error = 1.104222961956156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.402 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.402 Order of pole (three term test) = 3.28e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.402999999999956 y[1] (closed_form) = 0.5080245010056664 y[1] (numeric) = 0.5080245010056103 absolute error = 5.617728504603292e-14 relative error = 1.105798734801697e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.403 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.403 Order of pole (three term test) = 1.005e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.403999999999956 y[1] (closed_form) = 0.5073010771016788 y[1] (numeric) = 0.5073010771016225 absolute error = 5.628830734849544e-14 relative error = 1.109564120582648e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.404 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.404 Order of pole (three term test) = 3.423e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.404999999999956 y[1] (closed_form) = 0.5065791973252939 y[1] (numeric) = 0.5065791973252374 absolute error = 5.651035195342047e-14 relative error = 1.115528475148438e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.405 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.405 Order of pole (three term test) = 3.497e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.405999999999956 y[1] (closed_form) = 0.5058588572851077 y[1] (numeric) = 0.5058588572850512 absolute error = 5.651035195342047e-14 relative error = 1.117116981141848e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.406 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.406 Order of pole (three term test) = 7.145e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.406999999999955 y[1] (closed_form) = 0.5051400526053171 y[1] (numeric) = 0.5051400526052605 absolute error = 5.662137425588298e-14 relative error = 1.120904469242774e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.407 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.407 Order of pole (three term test) = 7.299e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.407999999999955 y[1] (closed_form) = 0.5044227789256518 y[1] (numeric) = 0.5044227789255952 absolute error = 5.662137425588298e-14 relative error = 1.122498360928077e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.408 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.408 Order of pole (three term test) = 1.118e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.408999999999955 y[1] (closed_form) = 0.5037070319013095 y[1] (numeric) = 0.5037070319012528 absolute error = 5.67323965583455e-14 relative error = 1.126297489717415e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.409 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.409 Order of pole (three term test) = 7.617e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.409999999999955 y[1] (closed_form) = 0.5029928072028891 y[1] (numeric) = 0.5029928072028322 absolute error = 5.684341886080801e-14 relative error = 1.130104010371652e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.41 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.41 Order of pole (three term test) = 3.89e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.410999999999955 y[1] (closed_form) = 0.5022801005163258 y[1] (numeric) = 0.5022801005162689 absolute error = 5.684341886080801e-14 relative error = 1.131707563217715e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.411 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.411999999999955 y[1] (closed_form) = 0.5015689075428259 y[1] (numeric) = 0.5015689075427689 absolute error = 5.695444116327053e-14 relative error = 1.135525753426164e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.412 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.412 Order of pole (three term test) = 4.059e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.412999999999955 y[1] (closed_form) = 0.500859223998802 y[1] (numeric) = 0.5008592239987449 absolute error = 5.706546346573305e-14 relative error = 1.139351353263079e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.413 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.413 Order of pole (three term test) = 4.146e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.413999999999955 y[1] (closed_form) = 0.500151045615808 y[1] (numeric) = 0.500151045615751 absolute error = 5.706546346573305e-14 relative error = 1.140964593915255e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.414 Order of pole (three term test) = 4.235e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.414999999999955 y[1] (closed_form) = 0.4994443681404758 y[1] (numeric) = 0.4994443681404187 absolute error = 5.71209746169643e-14 relative error = 1.14369043402444e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.415 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.415 Order of pole (three term test) = 4.326e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.415999999999954 y[1] (closed_form) = 0.4987391873344507 y[1] (numeric) = 0.4987391873343935 absolute error = 5.717648576819556e-14 relative error = 1.146420558484277e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.416 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.416 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.416999999999954 y[1] (closed_form) = 0.498035498974328 y[1] (numeric) = 0.4980354989742707 absolute error = 5.728750807065808e-14 relative error = 1.150269572924781e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.417 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.417 Order of pole (three term test) = 9.027e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.417999999999954 y[1] (closed_form) = 0.4973332988515901 y[1] (numeric) = 0.4973332988515327 absolute error = 5.734301922188934e-14 relative error = 1.153009849819068e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.418 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.418 Order of pole (three term test) = 4.61e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.418999999999954 y[1] (closed_form) = 0.4966325827725431 y[1] (numeric) = 0.4966325827724857 absolute error = 5.745404152435185e-14 relative error = 1.15687217305808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.419 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.419 Order of pole (three term test) = 7.063e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.419999999999954 y[1] (closed_form) = 0.4959333465582547 y[1] (numeric) = 0.4959333465581972 absolute error = 5.750955267558311e-14 relative error = 1.159622620150383e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.42 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.42 Order of pole (three term test) = 4.809e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.420999999999954 y[1] (closed_form) = 0.4952355860444914 y[1] (numeric) = 0.4952355860444339 absolute error = 5.756506382681437e-14 relative error = 1.162377370467129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.421 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.421 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.421999999999954 y[1] (closed_form) = 0.4945392970816569 y[1] (numeric) = 0.4945392970815992 absolute error = 5.767608612927688e-14 relative error = 1.166258909446251e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.422 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.422 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.422999999999954 y[1] (closed_form) = 0.4938444755347299 y[1] (numeric) = 0.4938444755346722 absolute error = 5.773159728050814e-14 relative error = 1.169023855496144e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.423 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.423 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.423999999999954 y[1] (closed_form) = 0.4931511172832035 y[1] (numeric) = 0.4931511172831457 absolute error = 5.77871084317394e-14 relative error = 1.171793115872711e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.424 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.424 Order of pole (three term test) = 2.616e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.424999999999953 y[1] (closed_form) = 0.4924592182210233 y[1] (numeric) = 0.4924592182209654 absolute error = 5.789813073420191e-14 relative error = 1.175693917221311e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.425 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.425 Order of pole (three term test) = 2.672e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.425999999999953 y[1] (closed_form) = 0.491768774256527 y[1] (numeric) = 0.491768774256469 absolute error = 5.795364188543317e-14 relative error = 1.178473398866154e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.426 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.426 Order of pole (three term test) = 2.729e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.426999999999953 y[1] (closed_form) = 0.491079781312384 y[1] (numeric) = 0.4910797813123259 absolute error = 5.806466418789569e-14 relative error = 1.182387595610657e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.427 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.427 Order of pole (three term test) = 5.573e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.427999999999953 y[1] (closed_form) = 0.490392235325535 y[1] (numeric) = 0.4903922353254768 absolute error = 5.81756864903582e-14 relative error = 1.186309290801468e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.428 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.428 Order of pole (three term test) = 2.846e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.428999999999953 y[1] (closed_form) = 0.4897061322471321 y[1] (numeric) = 0.4897061322470738 absolute error = 5.823119764158946e-14 relative error = 1.189104930632212e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.429 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.429 Order of pole (three term test) = 2.906e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.429999999999953 y[1] (closed_form) = 0.4890214680424793 y[1] (numeric) = 0.489021468042421 absolute error = 5.834221994405198e-14 relative error = 1.19304005563584e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.43 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.43 Order of pole (three term test) = 8.904e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.430999999999953 y[1] (closed_form) = 0.4883382386909733 y[1] (numeric) = 0.4883382386909148 absolute error = 5.845324224651449e-14 relative error = 1.196982697959569e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.431 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.431 Order of pole (three term test) = 3.031e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.431999999999953 y[1] (closed_form) = 0.4876564401860439 y[1] (numeric) = 0.4876564401859854 absolute error = 5.850875339774575e-14 relative error = 1.19979453927491e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.432 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.432 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.432999999999953 y[1] (closed_form) = 0.4869760685350962 y[1] (numeric) = 0.4869760685350377 absolute error = 5.856426454897701e-14 relative error = 1.202610730444063e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.433 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.433 Order of pole (three term test) = 3.161e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.433999999999952 y[1] (closed_form) = 0.4862971197594513 y[1] (numeric) = 0.4862971197593927 absolute error = 5.861977570020827e-14 relative error = 1.205431274797695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.434 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.434 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.434999999999952 y[1] (closed_form) = 0.4856195898942886 y[1] (numeric) = 0.4856195898942299 absolute error = 5.873079800267078e-14 relative error = 1.209399275170417e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.435 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.435 Order of pole (three term test) = 3.296e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.435999999999952 y[1] (closed_form) = 0.4849434749885876 y[1] (numeric) = 0.4849434749885288 absolute error = 5.878630915390204e-14 relative error = 1.212230129610167e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.436 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.436999999999952 y[1] (closed_form) = 0.4842687711050707 y[1] (numeric) = 0.4842687711050118 absolute error = 5.889733145636455e-14 relative error = 1.216211636401096e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.437 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.437 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.437999999999952 y[1] (closed_form) = 0.4835954743201454 y[1] (numeric) = 0.4835954743200864 absolute error = 5.895284260759581e-14 relative error = 1.219052818690532e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.438 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.438 Order of pole (three term test) = 3.509e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.438999999999952 y[1] (closed_form) = 0.4829235807238478 y[1] (numeric) = 0.4829235807237888 absolute error = 5.900835375882707e-14 relative error = 1.22189837303824e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.439 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.439 Order of pole (three term test) = 3.583e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.439999999999952 y[1] (closed_form) = 0.4822530864197854 y[1] (numeric) = 0.4822530864197263 absolute error = 5.917488721252084e-14 relative error = 1.22705046123875e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.44 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.44 Order of pole (three term test) = 3.658e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.440999999999952 y[1] (closed_form) = 0.4815839875250807 y[1] (numeric) = 0.4815839875250215 absolute error = 5.92303983637521e-14 relative error = 1.229907968247541e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.441 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.441 Order of pole (three term test) = 3.735e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.441999999999952 y[1] (closed_form) = 0.4809162801703152 y[1] (numeric) = 0.4809162801702558 absolute error = 5.934142066621462e-14 relative error = 1.233924138421744e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.442 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.442 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.442999999999951 y[1] (closed_form) = 0.480249960499473 y[1] (numeric) = 0.4802499604994137 absolute error = 5.934142066621462e-14 relative error = 1.235636138407964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.443 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.443 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.443999999999951 y[1] (closed_form) = 0.479585024669886 y[1] (numeric) = 0.4795850246698266 absolute error = 5.945244296867713e-14 relative error = 1.239664291219272e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.444 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.444 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.444999999999951 y[1] (closed_form) = 0.4789214688521773 y[1] (numeric) = 0.4789214688521178 absolute error = 5.950795411990839e-14 relative error = 1.242540959012133e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.445 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.445 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.445999999999951 y[1] (closed_form) = 0.4782592892302071 y[1] (numeric) = 0.4782592892301475 absolute error = 5.961897642237091e-14 relative error = 1.246582717051496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.446 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.446 Order of pole (three term test) = 4.144e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.446999999999951 y[1] (closed_form) = 0.4775984820010172 y[1] (numeric) = 0.4775984820009575 absolute error = 5.967448757360216e-14 relative error = 1.249469791519879e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.447 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.447 Order of pole (three term test) = 4.231e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.447999999999951 y[1] (closed_form) = 0.4769390433747767 y[1] (numeric) = 0.476939043374717 absolute error = 5.972999872483342e-14 relative error = 1.252361272463446e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.448 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.448 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.448999999999951 y[1] (closed_form) = 0.4762809695747278 y[1] (numeric) = 0.4762809695746679 absolute error = 5.984102102729594e-14 relative error = 1.25642267589923e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.449 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.449 Order of pole (three term test) = 4.41e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.449999999999951 y[1] (closed_form) = 0.4756242568371311 y[1] (numeric) = 0.4756242568370712 absolute error = 5.98965321785272e-14 relative error = 1.259324589053449e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.45 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.45 Order of pole (three term test) = 4.502e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.450999999999951 y[1] (closed_form) = 0.4749689014112125 y[1] (numeric) = 0.4749689014111525 absolute error = 6.000755448098971e-14 relative error = 1.263399652118216e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.451 Order of pole (three term test) = 4.596e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45199999999995 y[1] (closed_form) = 0.4743148995591092 y[1] (numeric) = 0.4743148995590492 absolute error = 6.000755448098971e-14 relative error = 1.265141671424799e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.452 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.452 Order of pole (three term test) = 9.384e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45299999999995 y[1] (closed_form) = 0.4736622475558167 y[1] (numeric) = 0.4736622475557566 absolute error = 6.006306563222097e-14 relative error = 1.268056847303269e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.453 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.453 Order of pole (three term test) = 2.395e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45399999999995 y[1] (closed_form) = 0.4730109416891355 y[1] (numeric) = 0.4730109416890753 absolute error = 6.022959908591474e-14 relative error = 1.27332359101109e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.454 Order of pole (three term test) = 2.445e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45499999999995 y[1] (closed_form) = 0.4723609782596184 y[1] (numeric) = 0.4723609782595581 absolute error = 6.0285110237146e-14 relative error = 1.276250854997853e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.455 Order of pole (three term test) = 7.488e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45599999999995 y[1] (closed_form) = 0.4717123535805178 y[1] (numeric) = 0.4717123535804575 absolute error = 6.034062138837726e-14 relative error = 1.279182555435822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.456 Order of pole (three term test) = 2.548e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45699999999995 y[1] (closed_form) = 0.4710650639777341 y[1] (numeric) = 0.4710650639776736 absolute error = 6.050715484207103e-14 relative error = 1.284475531493268e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.457 Order of pole (three term test) = 2.601e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45799999999995 y[1] (closed_form) = 0.4704191057897626 y[1] (numeric) = 0.4704191057897021 absolute error = 6.056266599330229e-14 relative error = 1.287419351125774e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.458 Order of pole (three term test) = 5.31e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45899999999995 y[1] (closed_form) = 0.4697744753676427 y[1] (numeric) = 0.4697744753675821 absolute error = 6.056266599330229e-14 relative error = 1.289185964092798e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.459 Order of pole (three term test) = 5.42e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.45999999999995 y[1] (closed_form) = 0.4691311690749057 y[1] (numeric) = 0.4691311690748451 absolute error = 6.061817714453355e-14 relative error = 1.292137064012788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.46 Order of pole (three term test) = 2.766e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.460999999999949 y[1] (closed_form) = 0.4684891832875241 y[1] (numeric) = 0.4684891832874634 absolute error = 6.072919944699606e-14 relative error = 1.296277515327925e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.461 Order of pole (three term test) = 2.824e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.461999999999949 y[1] (closed_form) = 0.4678485143938598 y[1] (numeric) = 0.467848514393799 absolute error = 6.078471059822732e-14 relative error = 1.299239149599084e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.462 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.462999999999949 y[1] (closed_form) = 0.4672091587946141 y[1] (numeric) = 0.4672091587945533 absolute error = 6.084022174945858e-14 relative error = 1.302205245856579e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.463 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.463 Order of pole (three term test) = 5.884e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.463999999999949 y[1] (closed_form) = 0.4665711129027766 y[1] (numeric) = 0.4665711129027157 absolute error = 6.095124405192109e-14 relative error = 1.306365575714972e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.464 Order of pole (three term test) = 3.003e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.464999999999949 y[1] (closed_form) = 0.4659343731435752 y[1] (numeric) = 0.4659343731435142 absolute error = 6.106226635438361e-14 relative error = 1.310533626064278e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.465 Order of pole (three term test) = 9.196e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.465999999999949 y[1] (closed_form) = 0.4652989359544257 y[1] (numeric) = 0.4652989359543646 absolute error = 6.106226635438361e-14 relative error = 1.312323361091125e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.466 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.466 Order of pole (three term test) = 3.129e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.466999999999949 y[1] (closed_form) = 0.4646647977848825 y[1] (numeric) = 0.4646647977848213 absolute error = 6.117328865684613e-14 relative error = 1.316503616122141e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.467 Order of pole (three term test) = 6.387e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.467999999999949 y[1] (closed_form) = 0.4640319550965882 y[1] (numeric) = 0.464031955096527 absolute error = 6.122879980807738e-14 relative error = 1.319495330775929e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.468 Order of pole (three term test) = 6.519e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.468999999999949 y[1] (closed_form) = 0.4634004043632253 y[1] (numeric) = 0.463400404363164 absolute error = 6.128431095930864e-14 relative error = 1.322491529620514e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.469 Order of pole (three term test) = 3.327e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.469999999999948 y[1] (closed_form) = 0.4627701420704661 y[1] (numeric) = 0.4627701420704047 absolute error = 6.13398221105399e-14 relative error = 1.325492215986564e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.47 Order of pole (three term test) = 3.395e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.470999999999948 y[1] (closed_form) = 0.4621411647159242 y[1] (numeric) = 0.4621411647158629 absolute error = 6.13398221105399e-14 relative error = 1.327296220154835e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.471 Order of pole (three term test) = 6.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.471999999999948 y[1] (closed_form) = 0.4615134688091062 y[1] (numeric) = 0.4615134688090448 absolute error = 6.145084441300241e-14 relative error = 1.331507064605736e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.472 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.472999999999948 y[1] (closed_form) = 0.4608870508713625 y[1] (numeric) = 0.460887050871301 absolute error = 6.150635556423367e-14 relative error = 1.334521233520197e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.473 Order of pole (three term test) = 7.219e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.473999999999948 y[1] (closed_form) = 0.4602619074358397 y[1] (numeric) = 0.4602619074357782 absolute error = 6.156186671546493e-14 relative error = 1.3375399032788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.474 Order of pole (three term test) = 7.367e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.474999999999948 y[1] (closed_form) = 0.4596380350474327 y[1] (numeric) = 0.459638035047371 absolute error = 6.167288901792745e-14 relative error = 1.341770791696189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.475 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.475 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.475999999999948 y[1] (closed_form) = 0.4590154302627362 y[1] (numeric) = 0.4590154302626745 absolute error = 6.17284001691587e-14 relative error = 1.344800111269156e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.476 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.476 Order of pole (three term test) = 7.673e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.476999999999948 y[1] (closed_form) = 0.4583940896499982 y[1] (numeric) = 0.4583940896499364 absolute error = 6.178391132038996e-14 relative error = 1.347833942788494e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.477 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.477 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.477999999999948 y[1] (closed_form) = 0.4577740097890718 y[1] (numeric) = 0.4577740097890101 absolute error = 6.178391132038996e-14 relative error = 1.349659657368012e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.478 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.478 Order of pole (three term test) = 7.991e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.478999999999947 y[1] (closed_form) = 0.4571551872713691 y[1] (numeric) = 0.4571551872713073 absolute error = 6.183942247162122e-14 relative error = 1.35270088130736e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.479 Order of pole (three term test) = 8.155e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.479999999999947 y[1] (closed_form) = 0.4565376186998134 y[1] (numeric) = 0.4565376186997514 absolute error = 6.195044477408373e-14 relative error = 1.356962542331434e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.48 Order of pole (three term test) = 8.322e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.480999999999947 y[1] (closed_form) = 0.4559213006887928 y[1] (numeric) = 0.4559213006887308 absolute error = 6.200595592531499e-14 relative error = 1.360014454942951e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.481 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.481 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.481999999999947 y[1] (closed_form) = 0.4553062298641145 y[1] (numeric) = 0.4553062298640524 absolute error = 6.206146707654625e-14 relative error = 1.363070896154186e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.482 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.482 Order of pole (three term test) = 4.333e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.482999999999947 y[1] (closed_form) = 0.4546924028629577 y[1] (numeric) = 0.4546924028628956 absolute error = 6.211697822777751e-14 relative error = 1.366131869295808e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.483 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.483 Order of pole (three term test) = 4.422e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.483999999999947 y[1] (closed_form) = 0.4540798163338283 y[1] (numeric) = 0.4540798163337662 absolute error = 6.217248937900877e-14 relative error = 1.369197377698486e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.484 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.484 Order of pole (three term test) = 9.024e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.484999999999947 y[1] (closed_form) = 0.4534684669365129 y[1] (numeric) = 0.4534684669364506 absolute error = 6.228351168147128e-14 relative error = 1.373491570477627e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.485 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.485 Order of pole (three term test) = 9.208e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.485999999999947 y[1] (closed_form) = 0.4528583513420329 y[1] (numeric) = 0.4528583513419706 absolute error = 6.23945339839338e-14 relative error = 1.377793603651768e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.486 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.486 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.486999999999947 y[1] (closed_form) = 0.4522494662326 y[1] (numeric) = 0.4522494662325375 absolute error = 6.245004513516506e-14 relative error = 1.380876038514679e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.487 Order of pole (three term test) = 2.397e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.487999999999946 y[1] (closed_form) = 0.4516418083015702 y[1] (numeric) = 0.4516418083015077 absolute error = 6.250555628639631e-14 relative error = 1.383963024181767e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.488 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.488 Order of pole (three term test) = 4.891e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.488999999999946 y[1] (closed_form) = 0.4510353742533998 y[1] (numeric) = 0.4510353742533372 absolute error = 6.256106743762757e-14 relative error = 1.387054563983703e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.489 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.489 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.489999999999946 y[1] (closed_form) = 0.4504301608035999 y[1] (numeric) = 0.4504301608035373 absolute error = 6.267208974009009e-14 relative error = 1.39138306431964e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.49 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.49 Order of pole (three term test) = 2.546e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.490999999999946 y[1] (closed_form) = 0.4498261646786924 y[1] (numeric) = 0.4498261646786297 absolute error = 6.267208974009009e-14 relative error = 1.393251319314792e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.491 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.491 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.491999999999946 y[1] (closed_form) = 0.4492233826161657 y[1] (numeric) = 0.449223382616103 absolute error = 6.272760089132134e-14 relative error = 1.396356541505283e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.492 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.492 Order of pole (three term test) = 2.651e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.492999999999946 y[1] (closed_form) = 0.4486218113644305 y[1] (numeric) = 0.4486218113643677 absolute error = 6.27831120425526e-14 relative error = 1.399466331153297e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.493 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.493 Order of pole (three term test) = 2.705e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.493999999999946 y[1] (closed_form) = 0.448021447682776 y[1] (numeric) = 0.4480214476827131 absolute error = 6.289413434501512e-14 relative error = 1.403819720469e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.494 Order of pole (three term test) = 5.519e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.494999999999946 y[1] (closed_form) = 0.4474222883413262 y[1] (numeric) = 0.4474222883412632 absolute error = 6.300515664747763e-14 relative error = 1.408181002360185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.495 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.495 Order of pole (three term test) = 2.815e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.495999999999946 y[1] (closed_form) = 0.4468243301209968 y[1] (numeric) = 0.4468243301209338 absolute error = 6.306066779870889e-14 relative error = 1.41130783504185e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.496 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.496 Order of pole (three term test) = 2.873e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.496999999999945 y[1] (closed_form) = 0.4462275698134514 y[1] (numeric) = 0.4462275698133883 absolute error = 6.311617894994015e-14 relative error = 1.414439250724161e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.497 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.497 Order of pole (three term test) = 5.861e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.497999999999945 y[1] (closed_form) = 0.4456320042210588 y[1] (numeric) = 0.4456320042209957 absolute error = 6.311617894994015e-14 relative error = 1.416329580283712e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.498 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.498 Order of pole (three term test) = 2.99e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.498999999999945 y[1] (closed_form) = 0.4450376301568504 y[1] (numeric) = 0.4450376301567872 absolute error = 6.317169010117141e-14 relative error = 1.419468508290119e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.499 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.499 Order of pole (three term test) = 3.05e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.499999999999945 y[1] (closed_form) = 0.4444444444444769 y[1] (numeric) = 0.4444444444444137 absolute error = 6.328271240363392e-14 relative error = 1.423861029081659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.5 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.5 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.500999999999945 y[1] (closed_form) = 0.4438524439181666 y[1] (numeric) = 0.4438524439181032 absolute error = 6.333822355486518e-14 relative error = 1.427010810073244e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.501 Order of pole (three term test) = 3.175e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.501999999999945 y[1] (closed_form) = 0.4432616254226824 y[1] (numeric) = 0.443261625422619 absolute error = 6.339373470609644e-14 relative error = 1.430165190718819e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.502 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.502 Order of pole (three term test) = 6.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.502999999999945 y[1] (closed_form) = 0.4426719858132807 y[1] (numeric) = 0.4426719858132172 absolute error = 6.350475700855895e-14 relative error = 1.434578176251372e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.503 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.503 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.503999999999945 y[1] (closed_form) = 0.4420835219556685 y[1] (numeric) = 0.442083521955605 absolute error = 6.356026815979021e-14 relative error = 1.437743435417254e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.504 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.504999999999945 y[1] (closed_form) = 0.4414962307259627 y[1] (numeric) = 0.4414962307258991 absolute error = 6.361577931102147e-14 relative error = 1.440913305339358e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.505 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.505 Order of pole (three term test) = 1.032e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.505999999999944 y[1] (closed_form) = 0.4409101090106479 y[1] (numeric) = 0.4409101090105841 absolute error = 6.372680161348399e-14 relative error = 1.445346802242291e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.506 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.506 Order of pole (three term test) = 7.016e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.506999999999944 y[1] (closed_form) = 0.4403251537065355 y[1] (numeric) = 0.4403251537064717 absolute error = 6.378231276471524e-14 relative error = 1.448527576219831e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.507 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.507 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.507999999999944 y[1] (closed_form) = 0.4397413617207229 y[1] (numeric) = 0.439741361720659 absolute error = 6.38378239159465e-14 relative error = 1.451712972055822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.508 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.508 Order of pole (three term test) = 3.651e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.508999999999944 y[1] (closed_form) = 0.4391587299705518 y[1] (numeric) = 0.4391587299704879 absolute error = 6.389333506717776e-14 relative error = 1.454902993080934e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.509 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.509999999999944 y[1] (closed_form) = 0.4385772553835683 y[1] (numeric) = 0.4385772553835043 absolute error = 6.400435736964027e-14 relative error = 1.459363352385059e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 Order of pole (three term test) = 3.799e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.510999999999944 y[1] (closed_form) = 0.4379969348974821 y[1] (numeric) = 0.437996934897418 absolute error = 6.405986852087153e-14 relative error = 1.462564310772299e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.511 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.511 Order of pole (three term test) = 7.75e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.511999999999944 y[1] (closed_form) = 0.437417765460126 y[1] (numeric) = 0.4374177654600619 absolute error = 6.411537967210279e-14 relative error = 1.465769905450889e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.512 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.512 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.512999999999944 y[1] (closed_form) = 0.4368397440294161 y[1] (numeric) = 0.4368397440293519 absolute error = 6.417089082333405e-14 relative error = 1.468980139751498e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.513 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.513 Order of pole (three term test) = 4.032e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.513999999999944 y[1] (closed_form) = 0.4362628675733116 y[1] (numeric) = 0.4362628675732473 absolute error = 6.428191312579656e-14 relative error = 1.473467441392874e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.514 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.514 Order of pole (three term test) = 4.112e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.514999999999944 y[1] (closed_form) = 0.4356871330697751 y[1] (numeric) = 0.4356871330697108 absolute error = 6.433742427702782e-14 relative error = 1.476688646362302e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.515 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.515 Order of pole (three term test) = 4.195e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.515999999999943 y[1] (closed_form) = 0.4351125375067332 y[1] (numeric) = 0.4351125375066688 absolute error = 6.439293542825908e-14 relative error = 1.479914502055979e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.516 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.516999999999943 y[1] (closed_form) = 0.4345390778820368 y[1] (numeric) = 0.4345390778819724 absolute error = 6.439293542825908e-14 relative error = 1.481867539787518e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.517 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.517 Order of pole (three term test) = 8.728e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.517999999999943 y[1] (closed_form) = 0.4339667512034223 y[1] (numeric) = 0.4339667512033578 absolute error = 6.450395773072159e-14 relative error = 1.486380178938762e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.518 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.518 Order of pole (three term test) = 4.451e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.518999999999943 y[1] (closed_form) = 0.4333955544884719 y[1] (numeric) = 0.4333955544884073 absolute error = 6.461498003318411e-14 relative error = 1.490900849443366e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.519 Order of pole (three term test) = 4.54e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.519999999999943 y[1] (closed_form) = 0.4328254847645754 y[1] (numeric) = 0.4328254847645108 absolute error = 6.467049118441537e-14 relative error = 1.49414702832462e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.52 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.520999999999943 y[1] (closed_form) = 0.4322565390688914 y[1] (numeric) = 0.4322565390688267 absolute error = 6.472600233564663e-14 relative error = 1.497397875693694e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.521 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.521 Order of pole (three term test) = 2.361e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.521999999999943 y[1] (closed_form) = 0.4316887144483084 y[1] (numeric) = 0.4316887144482436 absolute error = 6.478151348687788e-14 relative error = 1.500653394881255e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.522 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.522 Order of pole (three term test) = 4.817e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.522999999999943 y[1] (closed_form) = 0.431122007959407 y[1] (numeric) = 0.4311220079593422 absolute error = 6.483702463810914e-14 relative error = 1.503913589217973e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.523 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.523 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.523999999999943 y[1] (closed_form) = 0.4305564166684214 y[1] (numeric) = 0.4305564166683565 absolute error = 6.483702463810914e-14 relative error = 1.505889173358696e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.524 Order of pole (three term test) = 5.01e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.524999999999942 y[1] (closed_form) = 0.4299919376512016 y[1] (numeric) = 0.4299919376511366 absolute error = 6.494804694057166e-14 relative error = 1.510448016661555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.525 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.525 Order of pole (three term test) = 2.555e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.525999999999942 y[1] (closed_form) = 0.4294285679931754 y[1] (numeric) = 0.4294285679931104 absolute error = 6.494804694057166e-14 relative error = 1.512429581573712e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.526 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.526 Order of pole (three term test) = 5.211e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.526999999999942 y[1] (closed_form) = 0.4288663047893111 y[1] (numeric) = 0.4288663047892461 absolute error = 6.500355809180292e-14 relative error = 1.515706815058301e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.527 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.527 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.527999999999942 y[1] (closed_form) = 0.4283051451440801 y[1] (numeric) = 0.428305145144015 absolute error = 6.511458039426543e-14 relative error = 1.520284804712331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.528 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.528 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.528999999999942 y[1] (closed_form) = 0.4277450861714188 y[1] (numeric) = 0.4277450861713537 absolute error = 6.517009154549669e-14 relative error = 1.52357311988804e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.529 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.529 Order of pole (three term test) = 2.764e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.529999999999942 y[1] (closed_form) = 0.4271861249946927 y[1] (numeric) = 0.4271861249946274 absolute error = 6.522560269672795e-14 relative error = 1.526866133527589e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.53 Order of pole (three term test) = 2.819e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.530999999999942 y[1] (closed_form) = 0.4266282587466584 y[1] (numeric) = 0.4266282587465931 absolute error = 6.52811138479592e-14 relative error = 1.530163848961647e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.531 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.531 Order of pole (three term test) = 5.749e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.531999999999942 y[1] (closed_form) = 0.4260714845694276 y[1] (numeric) = 0.4260714845693622 absolute error = 6.539213615042172e-14 relative error = 1.534769129562957e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.532 Order of pole (three term test) = 2.931e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.532999999999942 y[1] (closed_form) = 0.42551579961443 y[1] (numeric) = 0.4255157996143646 absolute error = 6.539213615042172e-14 relative error = 1.536773398535967e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.533 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.533 Order of pole (three term test) = 8.967e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.533999999999941 y[1] (closed_form) = 0.4249612010423773 y[1] (numeric) = 0.4249612010423118 absolute error = 6.544764730165298e-14 relative error = 1.540085239337568e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.534 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.534 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.534999999999941 y[1] (closed_form) = 0.4244076860232264 y[1] (numeric) = 0.4244076860231608 absolute error = 6.555866960411549e-14 relative error = 1.544709762879452e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.535 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.535 Order of pole (three term test) = 6.217e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.535999999999941 y[1] (closed_form) = 0.4238552517361436 y[1] (numeric) = 0.423855251736078 absolute error = 6.561418075534675e-14 relative error = 1.548032741993547e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.536 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.536 Order of pole (three term test) = 3.17e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.536999999999941 y[1] (closed_form) = 0.4233038953694688 y[1] (numeric) = 0.4233038953694032 absolute error = 6.566969190657801e-14 relative error = 1.551360443996389e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.537 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.537 Order of pole (three term test) = 3.232e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.537999999999941 y[1] (closed_form) = 0.4227536141206796 y[1] (numeric) = 0.4227536141206139 absolute error = 6.572520305780927e-14 relative error = 1.554692872218647e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.538 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.538 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.538999999999941 y[1] (closed_form) = 0.4222044051963554 y[1] (numeric) = 0.4222044051962896 absolute error = 6.578071420904053e-14 relative error = 1.558030029990989e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.539 Order of pole (three term test) = 6.722e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.539999999999941 y[1] (closed_form) = 0.4216562658121424 y[1] (numeric) = 0.4216562658120765 absolute error = 6.583622536027178e-14 relative error = 1.561371920644085e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.54 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.54 Order of pole (three term test) = 3.427e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.540999999999941 y[1] (closed_form) = 0.4211091931927181 y[1] (numeric) = 0.4211091931926522 absolute error = 6.59472476627343e-14 relative error = 1.566036760269775e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.541 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.541 Order of pole (three term test) = 3.494e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.541999999999941 y[1] (closed_form) = 0.4205631845717561 y[1] (numeric) = 0.4205631845716901 absolute error = 6.600275881396556e-14 relative error = 1.569389838085179e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.542 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.542 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54299999999994 y[1] (closed_form) = 0.4200182371918913 y[1] (numeric) = 0.4200182371918252 absolute error = 6.605826996519681e-14 relative error = 1.572747659883567e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.543 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.543 Order of pole (three term test) = 7.266e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54399999999994 y[1] (closed_form) = 0.4194743483046849 y[1] (numeric) = 0.4194743483046188 absolute error = 6.616929226765933e-14 relative error = 1.577433579313825e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.544 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.544 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54499999999994 y[1] (closed_form) = 0.4189315151705899 y[1] (numeric) = 0.4189315151705237 absolute error = 6.616929226765933e-14 relative error = 1.579477548751973e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.545 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54599999999994 y[1] (closed_form) = 0.4183897350589166 y[1] (numeric) = 0.4183897350588504 absolute error = 6.622480341889059e-14 relative error = 1.582849622483328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.546 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.546 Order of pole (three term test) = 3.851e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54699999999994 y[1] (closed_form) = 0.4178490052477981 y[1] (numeric) = 0.4178490052477318 absolute error = 6.63358257213531e-14 relative error = 1.587554951387614e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.547 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.547 Order of pole (three term test) = 3.926e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54799999999994 y[1] (closed_form) = 0.4173093230241562 y[1] (numeric) = 0.4173093230240899 absolute error = 6.639133687258436e-14 relative error = 1.59093826113109e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.548 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.548 Order of pole (three term test) = 1.201e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54899999999994 y[1] (closed_form) = 0.4167706856836676 y[1] (numeric) = 0.4167706856836012 absolute error = 6.639133687258436e-14 relative error = 1.592994400834034e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.549 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.549 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.54999999999994 y[1] (closed_form) = 0.4162330905307296 y[1] (numeric) = 0.4162330905306632 absolute error = 6.644684802381562e-14 relative error = 1.596385523772046e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.55 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.55 Order of pole (three term test) = 8.323e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.55099999999994 y[1] (closed_form) = 0.4156965348784266 y[1] (numeric) = 0.4156965348783601 absolute error = 6.650235917504688e-14 relative error = 1.599781417338395e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.551 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.551 Order of pole (three term test) = 4.243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.551999999999939 y[1] (closed_form) = 0.4151610160484966 y[1] (numeric) = 0.4151610160484301 absolute error = 6.655787032627813e-14 relative error = 1.603182084863749e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.552 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.552 Order of pole (three term test) = 4.325e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.552999999999939 y[1] (closed_form) = 0.4146265313712977 y[1] (numeric) = 0.4146265313712311 absolute error = 6.661338147750939e-14 relative error = 1.606587529678779e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.553 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.553 Order of pole (three term test) = 4.41e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.553999999999939 y[1] (closed_form) = 0.4140930781857747 y[1] (numeric) = 0.414093078185708 absolute error = 6.672440377997191e-14 relative error = 1.61133830278702e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.554 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.554 Order of pole (three term test) = 4.496e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.554999999999939 y[1] (closed_form) = 0.4135606538394261 y[1] (numeric) = 0.4135606538393593 absolute error = 6.683542608243442e-14 relative error = 1.616097311529658e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.555 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.555 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.555999999999939 y[1] (closed_form) = 0.4130292556882713 y[1] (numeric) = 0.4130292556882044 absolute error = 6.689093723366568e-14 relative error = 1.619520562101557e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.556 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.556 Order of pole (three term test) = 4.673e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.556999999999939 y[1] (closed_form) = 0.4124988810968174 y[1] (numeric) = 0.4124988810967505 absolute error = 6.694644838489694e-14 relative error = 1.622948605506253e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.557 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.557 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.557999999999939 y[1] (closed_form) = 0.4119695274380268 y[1] (numeric) = 0.4119695274379598 absolute error = 6.70019595361282e-14 relative error = 1.626381445074415e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.558 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.558 Order of pole (three term test) = 4.856e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.558999999999939 y[1] (closed_form) = 0.4114411920932847 y[1] (numeric) = 0.4114411920932176 absolute error = 6.711298183859071e-14 relative error = 1.63116827212027e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.559 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.559 Order of pole (three term test) = 4.951e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.559999999999939 y[1] (closed_form) = 0.4109138724523664 y[1] (numeric) = 0.4109138724522992 absolute error = 6.716849298982197e-14 relative error = 1.634612445400179e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 Order of pole (three term test) = 2.523e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.560999999999938 y[1] (closed_form) = 0.4103875659134053 y[1] (numeric) = 0.4103875659133381 absolute error = 6.722400414105323e-14 relative error = 1.638061425945784e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.561 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.561 Order of pole (three term test) = 5.145e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.561999999999938 y[1] (closed_form) = 0.409862269882861 y[1] (numeric) = 0.4098622698827937 absolute error = 6.727951529228449e-14 relative error = 1.641515217087756e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.562 Order of pole (three term test) = 2.622e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.562999999999938 y[1] (closed_form) = 0.4093379817754867 y[1] (numeric) = 0.4093379817754194 absolute error = 6.733502644351574e-14 relative error = 1.644973822156762e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.563 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.563 Order of pole (three term test) = 8.019e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.563999999999938 y[1] (closed_form) = 0.4088146990142983 y[1] (numeric) = 0.408814699014231 absolute error = 6.7390537594747e-14 relative error = 1.648437244483472e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.564 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.564 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.564999999999938 y[1] (closed_form) = 0.408292419030542 y[1] (numeric) = 0.4082924190304745 absolute error = 6.744604874597826e-14 relative error = 1.651905487398555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.565 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.565 Order of pole (three term test) = 2.778e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.565999999999938 y[1] (closed_form) = 0.4077711392636629 y[1] (numeric) = 0.4077711392635954 absolute error = 6.755707104844078e-14 relative error = 1.656739885280569e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.566 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.566 Order of pole (three term test) = 2.831e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.566999999999938 y[1] (closed_form) = 0.407250857161274 y[1] (numeric) = 0.4072508571612063 absolute error = 6.761258219967203e-14 relative error = 1.660219518528773e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.567 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.567 Order of pole (three term test) = 5.772e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.567999999999938 y[1] (closed_form) = 0.4067315701791244 y[1] (numeric) = 0.4067315701790567 absolute error = 6.766809335090329e-14 relative error = 1.66370398346758e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.568 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.568 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.568999999999938 y[1] (closed_form) = 0.4062132757810687 y[1] (numeric) = 0.406213275781001 absolute error = 6.766809335090329e-14 relative error = 1.665826731555998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.569 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.569 Order of pole (three term test) = 2.999e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.569999999999937 y[1] (closed_form) = 0.405695971439036 y[1] (numeric) = 0.4056959714389681 absolute error = 6.783462680459706e-14 relative error = 1.67205571610638e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.57 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.57 Order of pole (three term test) = 6.113e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.570999999999937 y[1] (closed_form) = 0.4051796546329983 y[1] (numeric) = 0.4051796546329304 absolute error = 6.789013795582832e-14 relative error = 1.675556439706271e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.571 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.571 Order of pole (three term test) = 9.347e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.571999999999937 y[1] (closed_form) = 0.4046643228509411 y[1] (numeric) = 0.4046643228508731 absolute error = 6.794564910705958e-14 relative error = 1.679062009429665e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.572 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.572 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.572999999999937 y[1] (closed_form) = 0.4041499735888315 y[1] (numeric) = 0.4041499735887636 absolute error = 6.794564910705958e-14 relative error = 1.681198900094082e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.573 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.573 Order of pole (three term test) = 3.237e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.573999999999937 y[1] (closed_form) = 0.4036366043505891 y[1] (numeric) = 0.4036366043505211 absolute error = 6.800116025829084e-14 relative error = 1.684712425120559e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.574 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.574 Order of pole (three term test) = 3.299e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.574999999999937 y[1] (closed_form) = 0.4031242126480544 y[1] (numeric) = 0.4031242126479864 absolute error = 6.800116025829084e-14 relative error = 1.686853781657092e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.575 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.575 Order of pole (three term test) = 6.725e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.575999999999937 y[1] (closed_form) = 0.4026127960009599 y[1] (numeric) = 0.4026127960008918 absolute error = 6.80566714095221e-14 relative error = 1.690375270868436e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.576 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.576 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.576999999999937 y[1] (closed_form) = 0.402102351936899 y[1] (numeric) = 0.4021023519368309 absolute error = 6.816769371198461e-14 relative error = 1.695282143554385e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.577 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.577999999999937 y[1] (closed_form) = 0.4015928779912968 y[1] (numeric) = 0.4015928779912286 absolute error = 6.822320486321587e-14 relative error = 1.698815108586024e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.578 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.578 Order of pole (three term test) = 3.56e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.578999999999936 y[1] (closed_form) = 0.4010843717073803 y[1] (numeric) = 0.401084371707312 absolute error = 6.827871601444713e-14 relative error = 1.702352941945625e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.579 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.579 Order of pole (three term test) = 3.628e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.579999999999936 y[1] (closed_form) = 0.4005768306361482 y[1] (numeric) = 0.40057683063608 absolute error = 6.827871601444713e-14 relative error = 1.704509866584521e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.58 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.580999999999936 y[1] (closed_form) = 0.4000702523363425 y[1] (numeric) = 0.4000702523362741 absolute error = 6.838973831690964e-14 relative error = 1.709443226971392e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.581 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.581 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.581999999999936 y[1] (closed_form) = 0.399564634374418 y[1] (numeric) = 0.3995646343743495 absolute error = 6.850076061937216e-14 relative error = 1.714384976203437e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.582 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.582 Order of pole (three term test) = 1.152e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.582999999999936 y[1] (closed_form) = 0.3990599743245135 y[1] (numeric) = 0.399059974324445 absolute error = 6.850076061937216e-14 relative error = 1.71655302527704e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.583 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.583 Order of pole (three term test) = 3.915e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.583999999999936 y[1] (closed_form) = 0.3985562697684232 y[1] (numeric) = 0.3985562697683547 absolute error = 6.850076061937216e-14 relative error = 1.718722444365856e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.584 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.584 Order of pole (three term test) = 3.989e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.584999999999936 y[1] (closed_form) = 0.3980535182955671 y[1] (numeric) = 0.3980535182954985 absolute error = 6.866729407306593e-14 relative error = 1.725076928526941e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.585 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.585 Order of pole (three term test) = 4.066e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.585999999999936 y[1] (closed_form) = 0.3975517175029622 y[1] (numeric) = 0.3975517175028935 absolute error = 6.866729407306593e-14 relative error = 1.727254368421998e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.586 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.586 Order of pole (three term test) = 4.143e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.586999999999936 y[1] (closed_form) = 0.3970508649951942 y[1] (numeric) = 0.3970508649951254 absolute error = 6.877831637552845e-14 relative error = 1.732229354955842e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.587 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.587 Order of pole (three term test) = 4.222e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.587999999999935 y[1] (closed_form) = 0.3965509583843885 y[1] (numeric) = 0.3965509583843196 absolute error = 6.883382752675971e-14 relative error = 1.73581291562627e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.588 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.588 Order of pole (three term test) = 4.303e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.588999999999935 y[1] (closed_form) = 0.3960519952901819 y[1] (numeric) = 0.396051995290113 absolute error = 6.888933867799096e-14 relative error = 1.739401379041575e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.589 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.589 Order of pole (three term test) = 4.385e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.589999999999935 y[1] (closed_form) = 0.3955539733396944 y[1] (numeric) = 0.3955539733396255 absolute error = 6.894484982922222e-14 relative error = 1.742994748532425e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.59 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.590999999999935 y[1] (closed_form) = 0.3950568901675008 y[1] (numeric) = 0.3950568901674318 absolute error = 6.900036098045348e-14 relative error = 1.74659302742949e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.591 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.591 Order of pole (three term test) = 4.554e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.591999999999935 y[1] (closed_form) = 0.3945607434156025 y[1] (numeric) = 0.3945607434155335 absolute error = 6.900036098045348e-14 relative error = 1.748789308919498e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.592 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.592 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.592999999999935 y[1] (closed_form) = 0.3940655307333999 y[1] (numeric) = 0.3940655307333309 absolute error = 6.905587213168474e-14 relative error = 1.752395648590833e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.593 Order of pole (three term test) = 2.364e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.593999999999935 y[1] (closed_form) = 0.3935712497776644 y[1] (numeric) = 0.3935712497775953 absolute error = 6.916689443414725e-14 relative error = 1.757417353864666e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.594 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.594 Order of pole (three term test) = 4.818e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.594999999999935 y[1] (closed_form) = 0.3930778982125105 y[1] (numeric) = 0.3930778982124412 absolute error = 6.927791673660977e-14 relative error = 1.762447521258392e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.595 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.595 Order of pole (three term test) = 2.455e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.595999999999935 y[1] (closed_form) = 0.3925854737093682 y[1] (numeric) = 0.3925854737092989 absolute error = 6.927791673660977e-14 relative error = 1.764658179581457e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.596 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.596 Order of pole (three term test) = 5.003e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.596999999999934 y[1] (closed_form) = 0.392093973946956 y[1] (numeric) = 0.3920939739468867 absolute error = 6.933342788784103e-14 relative error = 1.768285984859862e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.597 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.597 Order of pole (three term test) = 2.549e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.597999999999934 y[1] (closed_form) = 0.391603396611253 y[1] (numeric) = 0.3916033966111837 absolute error = 6.938893903907228e-14 relative error = 1.771918722859166e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.598 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.598 Order of pole (three term test) = 1.039e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.598999999999934 y[1] (closed_form) = 0.391113739395472 y[1] (numeric) = 0.3911137393954026 absolute error = 6.938893903907228e-14 relative error = 1.774137087240245e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.599 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.599 Order of pole (three term test) = 5.293e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.599999999999934 y[1] (closed_form) = 0.3906250000000322 y[1] (numeric) = 0.3906249999999627 absolute error = 6.94999613415348e-14 relative error = 1.779199010343144e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.6 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.6 Order of pole (three term test) = 5.393e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.600999999999934 y[1] (closed_form) = 0.3901371761325321 y[1] (numeric) = 0.3901371761324626 absolute error = 6.94999613415348e-14 relative error = 1.781423704105687e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.601 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.601 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.601999999999934 y[1] (closed_form) = 0.389650265507723 y[1] (numeric) = 0.3896502655076535 absolute error = 6.955547249276606e-14 relative error = 1.785074428273101e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.602 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.602 Order of pole (three term test) = 5.599e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.602999999999934 y[1] (closed_form) = 0.3891642658474821 y[1] (numeric) = 0.3891642658474124 absolute error = 6.966649479522857e-14 relative error = 1.790156520242577e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.603 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.603 Order of pole (three term test) = 8.558e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.603999999999934 y[1] (closed_form) = 0.3886791748807853 y[1] (numeric) = 0.3886791748807156 absolute error = 6.972200594645983e-14 relative error = 1.793818924511322e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.604 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.604 Order of pole (three term test) = 8.719e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.604999999999934 y[1] (closed_form) = 0.3881949903436818 y[1] (numeric) = 0.3881949903436119 absolute error = 6.983302824892235e-14 relative error = 1.798916265949153e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.605 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.605 Order of pole (three term test) = 2.961e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.605999999999933 y[1] (closed_form) = 0.3877117099792663 y[1] (numeric) = 0.3877117099791964 absolute error = 6.98885394001536e-14 relative error = 1.802590368082797e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.606 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.606 Order of pole (three term test) = 3.017e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.606999999999933 y[1] (closed_form) = 0.3872293315376539 y[1] (numeric) = 0.387229331537584 absolute error = 6.98885394001536e-14 relative error = 1.804835886853723e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.607 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.607 Order of pole (three term test) = 3.074e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.607999999999933 y[1] (closed_form) = 0.3867478527759535 y[1] (numeric) = 0.3867478527758835 absolute error = 6.994405055138486e-14 relative error = 1.80851813524881e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.608 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.608 Order of pole (three term test) = 6.264e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.608999999999933 y[1] (closed_form) = 0.3862672714582412 y[1] (numeric) = 0.3862672714581712 absolute error = 6.999956170261612e-14 relative error = 1.812205353002155e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.609 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.609 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.609999999999933 y[1] (closed_form) = 0.3857875853555354 y[1] (numeric) = 0.3857875853554653 absolute error = 7.011058400507864e-14 relative error = 1.817336447995492e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.61 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.61 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.610999999999933 y[1] (closed_form) = 0.3853087922457697 y[1] (numeric) = 0.3853087922456995 absolute error = 7.022160630754115e-14 relative error = 1.822476095036788e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.611 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.611 Order of pole (three term test) = 3.312e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.611999999999933 y[1] (closed_form) = 0.3848308899137683 y[1] (numeric) = 0.3848308899136982 absolute error = 7.016609515630989e-14 relative error = 1.82329685571843e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.612 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.612 Order of pole (three term test) = 3.374e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.612999999999933 y[1] (closed_form) = 0.38435387615122 y[1] (numeric) = 0.3843538761511497 absolute error = 7.022160630754115e-14 relative error = 1.827003984211498e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.613 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.613 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.613999999999933 y[1] (closed_form) = 0.383877748756652 y[1] (numeric) = 0.3838777487565818 absolute error = 7.022160630754115e-14 relative error = 1.829270035447042e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.614 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.614 Order of pole (three term test) = 7.004e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.614999999999932 y[1] (closed_form) = 0.3834025055354057 y[1] (numeric) = 0.3834025055353354 absolute error = 7.033262861000367e-14 relative error = 1.834433202563115e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.615 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.615 Order of pole (three term test) = 3.568e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.615999999999932 y[1] (closed_form) = 0.3829281442996105 y[1] (numeric) = 0.3829281442995401 absolute error = 7.033262861000367e-14 relative error = 1.836705649793504e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.616 Order of pole (three term test) = 7.269e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.616999999999932 y[1] (closed_form) = 0.382454662868159 y[1] (numeric) = 0.3824546628680885 absolute error = 7.044365091246618e-14 relative error = 1.841882391606499e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.617 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.617 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.617999999999932 y[1] (closed_form) = 0.3819820590666818 y[1] (numeric) = 0.3819820590666113 absolute error = 7.044365091246618e-14 relative error = 1.844161243713517e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.618 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.618 Order of pole (three term test) = 3.772e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.618999999999932 y[1] (closed_form) = 0.3815103307275226 y[1] (numeric) = 0.3815103307274521 absolute error = 7.049916206369744e-14 relative error = 1.847896541340278e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.619 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.619 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.619999999999932 y[1] (closed_form) = 0.3810394756897135 y[1] (numeric) = 0.3810394756896429 absolute error = 7.05546732149287e-14 relative error = 1.851636843852433e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.62 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.62 Order of pole (three term test) = 3.914e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.620999999999932 y[1] (closed_form) = 0.3805694917989497 y[1] (numeric) = 0.3805694917988792 absolute error = 7.05546732149287e-14 relative error = 1.853923520811329e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.621 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.621 Order of pole (three term test) = 3.988e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.621999999999932 y[1] (closed_form) = 0.3801003769075657 y[1] (numeric) = 0.3801003769074951 absolute error = 7.061018436615996e-14 relative error = 1.857672042859648e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.622 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.622 Order of pole (three term test) = 4.062e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.622999999999932 y[1] (closed_form) = 0.37963212887451 y[1] (numeric) = 0.3796321288744394 absolute error = 7.066569551739121e-14 relative error = 1.861425578675145e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.623 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.623 Order of pole (three term test) = 8.276e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.623999999999931 y[1] (closed_form) = 0.3791647455653211 y[1] (numeric) = 0.3791647455652504 absolute error = 7.077671781985373e-14 relative error = 1.866648169368388e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.624 Order of pole (three term test) = 8.43e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.624999999999931 y[1] (closed_form) = 0.378698224852103 y[1] (numeric) = 0.3786982248520322 absolute error = 7.083222897108499e-14 relative error = 1.870413546267555e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.625 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.625 Order of pole (three term test) = 4.294e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.625999999999931 y[1] (closed_form) = 0.378232564613501 y[1] (numeric) = 0.3782325646134301 absolute error = 7.083222897108499e-14 relative error = 1.872716302031405e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.626 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.626 Order of pole (three term test) = 8.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.626999999999931 y[1] (closed_form) = 0.3777677627346777 y[1] (numeric) = 0.3777677627346068 absolute error = 7.09432512735475e-14 relative error = 1.877959378004786e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.627 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.627 Order of pole (three term test) = 4.455e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.627999999999931 y[1] (closed_form) = 0.3773038171072889 y[1] (numeric) = 0.3773038171072179 absolute error = 7.099876242477876e-14 relative error = 1.881739839504189e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.628 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.628 Order of pole (three term test) = 4.538e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.628999999999931 y[1] (closed_form) = 0.3768407256294596 y[1] (numeric) = 0.3768407256293886 absolute error = 7.105427357601002e-14 relative error = 1.885525335865008e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.629 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.629 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.629999999999931 y[1] (closed_form) = 0.3763784862057604 y[1] (numeric) = 0.3763784862056894 absolute error = 7.105427357601002e-14 relative error = 1.88784099464085e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.63 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.63 Order of pole (three term test) = 4.708e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.630999999999931 y[1] (closed_form) = 0.3759170967471837 y[1] (numeric) = 0.3759170967471126 absolute error = 7.110978472724128e-14 relative error = 1.891634760497868e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.631 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.631 Order of pole (three term test) = 2.398e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.631999999999931 y[1] (closed_form) = 0.37545655517112 y[1] (numeric) = 0.3754565551710488 absolute error = 7.116529587847253e-14 relative error = 1.895433570098087e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.632 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.632 Order of pole (three term test) = 7.327e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.632999999999931 y[1] (closed_form) = 0.3749968594013345 y[1] (numeric) = 0.3749968594012632 absolute error = 7.127631818093505e-14 relative error = 1.900717736535833e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.633 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.633 Order of pole (three term test) = 4.975e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63399999999993 y[1] (closed_form) = 0.3745380073679436 y[1] (numeric) = 0.3745380073678723 absolute error = 7.133182933216631e-14 relative error = 1.904528457163772e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.634 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.634 Order of pole (three term test) = 2.534e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63499999999993 y[1] (closed_form) = 0.3740799970073919 y[1] (numeric) = 0.3740799970073206 absolute error = 7.133182933216631e-14 relative error = 1.90686029466464e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.635 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.635 Order of pole (three term test) = 2.581e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63599999999993 y[1] (closed_form) = 0.3736228262624287 y[1] (numeric) = 0.3736228262623573 absolute error = 7.138734048339757e-14 relative error = 1.910679312544353e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.636 Order of pole (three term test) = 2.628e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63699999999993 y[1] (closed_form) = 0.3731664930820848 y[1] (numeric) = 0.3731664930820134 absolute error = 7.138734048339757e-14 relative error = 1.913015820198375e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.637 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.637 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63799999999993 y[1] (closed_form) = 0.37271099542165 y[1] (numeric) = 0.3727109954215785 absolute error = 7.149836278586008e-14 relative error = 1.918332532824088e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.638 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.638 Order of pole (three term test) = 2.727e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63899999999993 y[1] (closed_form) = 0.3722563312426496 y[1] (numeric) = 0.3722563312425781 absolute error = 7.149836278586008e-14 relative error = 1.92067553417258e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.639 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.639 Order of pole (three term test) = 2.777e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.63999999999993 y[1] (closed_form) = 0.3718024985128218 y[1] (numeric) = 0.3718024985127503 absolute error = 7.149836278586008e-14 relative error = 1.923019965488328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.64 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.64 Order of pole (three term test) = 5.656e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64099999999993 y[1] (closed_form) = 0.3713494952060956 y[1] (numeric) = 0.3713494952060239 absolute error = 7.16093850883226e-14 relative error = 1.928355525260107e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.641 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.641 Order of pole (three term test) = 2.88e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.64199999999993 y[1] (closed_form) = 0.3708973193025669 y[1] (numeric) = 0.3708973193024952 absolute error = 7.166489623955385e-14 relative error = 1.932203133048039e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.642 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.642 Order of pole (three term test) = 2.934e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.642999999999929 y[1] (closed_form) = 0.3704459687884772 y[1] (numeric) = 0.3704459687884055 absolute error = 7.172040739078511e-14 relative error = 1.936055820106308e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.643 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.643 Order of pole (three term test) = 2.988e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.643999999999929 y[1] (closed_form) = 0.3699954416561906 y[1] (numeric) = 0.3699954416561189 absolute error = 7.172040739078511e-14 relative error = 1.938413269897243e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.644 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.644 Order of pole (three term test) = 3.043e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.644999999999929 y[1] (closed_form) = 0.3695457359041717 y[1] (numeric) = 0.3695457359040998 absolute error = 7.183142969324763e-14 relative error = 1.943776445356537e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.645 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.645 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.645999999999929 y[1] (closed_form) = 0.3690968495369629 y[1] (numeric) = 0.369096849536891 absolute error = 7.183142969324763e-14 relative error = 1.946140417707741e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.646 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.646 Order of pole (three term test) = 6.311e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.646999999999929 y[1] (closed_form) = 0.368648780565163 y[1] (numeric) = 0.3686487805650911 absolute error = 7.188694084447889e-14 relative error = 1.950011627171842e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.647 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.647 Order of pole (three term test) = 3.214e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.647999999999929 y[1] (closed_form) = 0.3682015270054045 y[1] (numeric) = 0.3682015270053327 absolute error = 7.188694084447889e-14 relative error = 1.952380301872668e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.648 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.648 Order of pole (three term test) = 3.273e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.648999999999929 y[1] (closed_form) = 0.3677550868803323 y[1] (numeric) = 0.3677550868802603 absolute error = 7.194245199571014e-14 relative error = 1.956259874091701e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.649 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.649 Order of pole (three term test) = 9.998e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.649999999999929 y[1] (closed_form) = 0.3673094582185809 y[1] (numeric) = 0.3673094582185089 absolute error = 7.19979631469414e-14 relative error = 1.96014454667531e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.65 Order of pole (three term test) = 6.788e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.650999999999929 y[1] (closed_form) = 0.3668646390547536 y[1] (numeric) = 0.3668646390546816 absolute error = 7.19979631469414e-14 relative error = 1.96252119943879e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.651 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.651 Order of pole (three term test) = 1.037e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.651999999999928 y[1] (closed_form) = 0.3664206274294005 y[1] (numeric) = 0.3664206274293285 absolute error = 7.205347429817266e-14 relative error = 1.966414249210232e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.652 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.652 Order of pole (three term test) = 3.52e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.652999999999928 y[1] (closed_form) = 0.3659774213889966 y[1] (numeric) = 0.3659774213889245 absolute error = 7.210898544940392e-14 relative error = 1.970312408228032e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.653 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.653 Order of pole (three term test) = 3.584e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.653999999999928 y[1] (closed_form) = 0.3655350189859206 y[1] (numeric) = 0.3655350189858484 absolute error = 7.216449660063518e-14 relative error = 1.974215679822861e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.654 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.654 Order of pole (three term test) = 3.65e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.654999999999928 y[1] (closed_form) = 0.3650934182784337 y[1] (numeric) = 0.3650934182783615 absolute error = 7.222000775186643e-14 relative error = 1.978124067325387e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.655 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.655 Order of pole (three term test) = 3.716e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.655999999999928 y[1] (closed_form) = 0.3646526173306578 y[1] (numeric) = 0.3646526173305856 absolute error = 7.222000775186643e-14 relative error = 1.980515271782052e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.656 Order of pole (three term test) = 3.784e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.656999999999928 y[1] (closed_form) = 0.3642126142125549 y[1] (numeric) = 0.3642126142124826 absolute error = 7.227551890309769e-14 relative error = 1.98443206200754e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.657 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.657 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.657999999999928 y[1] (closed_form) = 0.3637734069999051 y[1] (numeric) = 0.3637734069998328 absolute error = 7.227551890309769e-14 relative error = 1.986827995459178e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.658 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.658 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.658999999999928 y[1] (closed_form) = 0.3633349937742866 y[1] (numeric) = 0.3633349937742142 absolute error = 7.238654120556021e-14 relative error = 1.992281020157631e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.659 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.659 Order of pole (three term test) = 3.996e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.659999999999928 y[1] (closed_form) = 0.3628973726230539 y[1] (numeric) = 0.3628973726229814 absolute error = 7.244205235679146e-14 relative error = 1.996213194743571e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.66 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.66 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.660999999999927 y[1] (closed_form) = 0.3624605416393175 y[1] (numeric) = 0.362460541639245 absolute error = 7.249756350802272e-14 relative error = 2.000150504111001e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.661 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.661 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.661999999999927 y[1] (closed_form) = 0.3620244989219227 y[1] (numeric) = 0.3620244989218501 absolute error = 7.260858581048524e-14 relative error = 2.005626305034804e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.662 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.662 Order of pole (three term test) = 4.218e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.662999999999927 y[1] (closed_form) = 0.3615892425754293 y[1] (numeric) = 0.3615892425753567 absolute error = 7.260858581048524e-14 relative error = 2.008040540513003e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.663 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.663 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.663999999999927 y[1] (closed_form) = 0.3611547707100908 y[1] (numeric) = 0.3611547707100181 absolute error = 7.26640969617165e-14 relative error = 2.011993274208913e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.664 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.664999999999927 y[1] (closed_form) = 0.3607210814418338 y[1] (numeric) = 0.3607210814417611 absolute error = 7.271960811294775e-14 relative error = 2.015951156008989e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.665 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.665 Order of pole (three term test) = 4.453e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.665999999999927 y[1] (closed_form) = 0.3602881728922377 y[1] (numeric) = 0.360288172892165 absolute error = 7.277511926417901e-14 relative error = 2.019914189243899e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.666 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.666 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.666999999999927 y[1] (closed_form) = 0.3598560431885145 y[1] (numeric) = 0.3598560431884417 absolute error = 7.283063041541027e-14 relative error = 2.023882377244312e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.667 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.667 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.667999999999927 y[1] (closed_form) = 0.3594246904634882 y[1] (numeric) = 0.3594246904634153 absolute error = 7.288614156664153e-14 relative error = 2.027855723340898e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.668 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.668 Order of pole (three term test) = 2.35e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.668999999999927 y[1] (closed_form) = 0.3589941128555749 y[1] (numeric) = 0.3589941128555019 absolute error = 7.294165271787278e-14 relative error = 2.031834230864326e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.669 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.669 Order of pole (three term test) = 4.785e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.669999999999926 y[1] (closed_form) = 0.3585643085087626 y[1] (numeric) = 0.3585643085086896 absolute error = 7.299716386910404e-14 relative error = 2.035817903145263e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.67 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.67 Order of pole (three term test) = 2.436e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.670999999999926 y[1] (closed_form) = 0.3581352755725914 y[1] (numeric) = 0.3581352755725183 absolute error = 7.30526750203353e-14 relative error = 2.039806743514381e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.671 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.671 Order of pole (three term test) = 4.96e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.671999999999926 y[1] (closed_form) = 0.3577070122021332 y[1] (numeric) = 0.3577070122020601 absolute error = 7.310818617156656e-14 relative error = 2.043800755302347e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.672 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.672999999999926 y[1] (closed_form) = 0.3572795165579721 y[1] (numeric) = 0.357279516557899 absolute error = 7.310818617156656e-14 relative error = 2.046246224129786e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.673 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.673 Order of pole (three term test) = 5.141e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.673999999999926 y[1] (closed_form) = 0.3568527868061848 y[1] (numeric) = 0.3568527868061117 absolute error = 7.316369732279782e-14 relative error = 2.050248730789224e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.674 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.674 Order of pole (three term test) = 2.617e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.674999999999926 y[1] (closed_form) = 0.3564268211183207 y[1] (numeric) = 0.3564268211182475 absolute error = 7.321920847402907e-14 relative error = 2.054256417749296e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.675 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.675 Order of pole (three term test) = 2.664e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.675999999999926 y[1] (closed_form) = 0.3560016176713822 y[1] (numeric) = 0.3560016176713089 absolute error = 7.327471962526033e-14 relative error = 2.05826928834067e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.676 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.676 Order of pole (three term test) = 2.713e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.676999999999926 y[1] (closed_form) = 0.3555771746478056 y[1] (numeric) = 0.3555771746477323 absolute error = 7.333023077649159e-14 relative error = 2.062287345894015e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.677 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.677 Order of pole (three term test) = 2.762e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.677999999999926 y[1] (closed_form) = 0.3551534902354414 y[1] (numeric) = 0.3551534902353681 absolute error = 7.333023077649159e-14 relative error = 2.064747575136567e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.678 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.678 Order of pole (three term test) = 8.434e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.678999999999925 y[1] (closed_form) = 0.3547305626275349 y[1] (numeric) = 0.3547305626274616 absolute error = 7.338574192772285e-14 relative error = 2.068774153096514e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.679 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.679 Order of pole (three term test) = 2.862e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.679999999999925 y[1] (closed_form) = 0.3543083900227072 y[1] (numeric) = 0.3543083900226338 absolute error = 7.344125307895411e-14 relative error = 2.072805926900217e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.68 Order of pole (three term test) = 5.827e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.680999999999925 y[1] (closed_form) = 0.3538869706249357 y[1] (numeric) = 0.3538869706248622 absolute error = 7.355227538141662e-14 relative error = 2.078411512340487e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.681 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.681 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.681999999999925 y[1] (closed_form) = 0.3534663026435352 y[1] (numeric) = 0.3534663026434617 absolute error = 7.355227538141662e-14 relative error = 2.080885075361564e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.682 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.682 Order of pole (three term test) = 9.059e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.682999999999925 y[1] (closed_form) = 0.353046384293139 y[1] (numeric) = 0.3530463842930654 absolute error = 7.360778653264788e-14 relative error = 2.084932456680547e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.683 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.683 Order of pole (three term test) = 9.222e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.683999999999925 y[1] (closed_form) = 0.3526272137936797 y[1] (numeric) = 0.352627213793606 absolute error = 7.371880883511039e-14 relative error = 2.090559263478822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.684 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.684 Order of pole (three term test) = 6.258e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.684999999999925 y[1] (closed_form) = 0.3522087893703702 y[1] (numeric) = 0.3522087893702964 absolute error = 7.377431998634165e-14 relative error = 2.094618936632022e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.685 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.685 Order of pole (three term test) = 6.371e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.685999999999925 y[1] (closed_form) = 0.3517911092536855 y[1] (numeric) = 0.3517911092536117 absolute error = 7.382983113757291e-14 relative error = 2.098683826723215e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.686 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.686 Order of pole (three term test) = 3.243e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.686999999999925 y[1] (closed_form) = 0.3513741716793435 y[1] (numeric) = 0.3513741716792696 absolute error = 7.388534228880417e-14 relative error = 2.102753937083069e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.687 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.687 Order of pole (three term test) = 6.602e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.687999999999924 y[1] (closed_form) = 0.3509579748882864 y[1] (numeric) = 0.3509579748882125 absolute error = 7.388534228880417e-14 relative error = 2.105247567385316e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.688 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.688 Order of pole (three term test) = 3.36e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.688999999999924 y[1] (closed_form) = 0.3505425171266625 y[1] (numeric) = 0.3505425171265885 absolute error = 7.394085344003543e-14 relative error = 2.109326253662924e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.689 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.689 Order of pole (three term test) = 6.84e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.689999999999924 y[1] (closed_form) = 0.3501277966458071 y[1] (numeric) = 0.3501277966457331 absolute error = 7.399636459126668e-14 relative error = 2.113410169090978e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.69 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.69 Order of pole (three term test) = 6.963e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.690999999999924 y[1] (closed_form) = 0.3497138117022249 y[1] (numeric) = 0.3497138117021509 absolute error = 7.405187574249794e-14 relative error = 2.117499317000147e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.691 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.691 Order of pole (three term test) = 7.088e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.691999999999924 y[1] (closed_form) = 0.3493005605575709 y[1] (numeric) = 0.3493005605574969 absolute error = 7.399636459126668e-14 relative error = 2.118415283191931e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.692 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 Order of pole (three term test) = 7.214e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.692999999999924 y[1] (closed_form) = 0.3488880414786328 y[1] (numeric) = 0.3488880414785587 absolute error = 7.41073868937292e-14 relative error = 2.124102235767453e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.693 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.693 Order of pole (three term test) = 3.672e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.693999999999924 y[1] (closed_form) = 0.3484762527373123 y[1] (numeric) = 0.3484762527372381 absolute error = 7.416289804496046e-14 relative error = 2.12820522094129e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.694 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.694 Order of pole (three term test) = 3.737e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.694999999999924 y[1] (closed_form) = 0.3480651926106073 y[1] (numeric) = 0.3480651926105331 absolute error = 7.421840919619171e-14 relative error = 2.132313450808695e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.695 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.695 Order of pole (three term test) = 7.608e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.695999999999924 y[1] (closed_form) = 0.3476548593805938 y[1] (numeric) = 0.3476548593805195 absolute error = 7.427392034742297e-14 relative error = 2.136426928700337e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.696 Order of pole (three term test) = 7.744e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.696999999999923 y[1] (closed_form) = 0.347245251334408 y[1] (numeric) = 0.3472452513343337 absolute error = 7.432943149865423e-14 relative error = 2.140545657946886e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.697 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.697 Order of pole (three term test) = 1.182e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.697999999999923 y[1] (closed_form) = 0.3468363667642284 y[1] (numeric) = 0.346836366764154 absolute error = 7.432943149865423e-14 relative error = 2.143069142146265e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.698 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.698 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.698999999999923 y[1] (closed_form) = 0.3464282039672578 y[1] (numeric) = 0.3464282039671834 absolute error = 7.438494264988549e-14 relative error = 2.147196498380827e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.699 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.699 Order of pole (three term test) = 1.225e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.699999999999923 y[1] (closed_form) = 0.346020761245706 y[1] (numeric) = 0.3460207612456316 absolute error = 7.438494264988549e-14 relative error = 2.149724842581496e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.7 Order of pole (three term test) = 4.156e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.700999999999923 y[1] (closed_form) = 0.3456140369067718 y[1] (numeric) = 0.3456140369066974 absolute error = 7.444045380111675e-14 relative error = 2.153860834685855e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.701 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.701 Order of pole (three term test) = 4.23e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.701999999999923 y[1] (closed_form) = 0.3452080292626255 y[1] (numeric) = 0.345208029262551 absolute error = 7.4495964952348e-14 relative error = 2.15800209257802e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.702 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.702 Order of pole (three term test) = 8.61e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.702999999999923 y[1] (closed_form) = 0.3448027366303913 y[1] (numeric) = 0.3448027366303168 absolute error = 7.455147610357926e-14 relative error = 2.162148619588659e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.703 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.703 Order of pole (three term test) = 4.381e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.703999999999923 y[1] (closed_form) = 0.3443981573321303 y[1] (numeric) = 0.3443981573320556 absolute error = 7.466249840604178e-14 relative error = 2.167912249717377e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.704 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.704 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.704999999999923 y[1] (closed_form) = 0.3439942896948223 y[1] (numeric) = 0.3439942896947477 absolute error = 7.466249840604178e-14 relative error = 2.170457494288039e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.705 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.705 Order of pole (three term test) = 4.538e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.705999999999922 y[1] (closed_form) = 0.3435911320503495 y[1] (numeric) = 0.3435911320502748 absolute error = 7.471800955727304e-14 relative error = 2.174619848638117e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.706 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.706 Order of pole (three term test) = 4.619e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.706999999999922 y[1] (closed_form) = 0.3431886827354784 y[1] (numeric) = 0.3431886827354036 absolute error = 7.471800955727304e-14 relative error = 2.177169974304307e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.707 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.707 Order of pole (three term test) = 7.051e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.707999999999922 y[1] (closed_form) = 0.3427869400918432 y[1] (numeric) = 0.3427869400917685 absolute error = 7.477352070850429e-14 relative error = 2.181341001161542e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.708 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.708 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.708999999999922 y[1] (closed_form) = 0.3423859024659287 y[1] (numeric) = 0.3423859024658539 absolute error = 7.482903185973555e-14 relative error = 2.185517316011044e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.709 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.709 Order of pole (three term test) = 2.434e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.709999999999922 y[1] (closed_form) = 0.3419855682090527 y[1] (numeric) = 0.3419855682089779 absolute error = 7.482903185973555e-14 relative error = 2.188075720610328e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.71 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.71 Order of pole (three term test) = 2.478e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.710999999999922 y[1] (closed_form) = 0.34158593567735 y[1] (numeric) = 0.3415859356772751 absolute error = 7.488454301096681e-14 relative error = 2.192260722399886e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.711 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.711 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.711999999999922 y[1] (closed_form) = 0.3411870032317544 y[1] (numeric) = 0.3411870032316795 absolute error = 7.494005416219807e-14 relative error = 2.196451021063494e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.712 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.712 Order of pole (three term test) = 5.132e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.712999999999922 y[1] (closed_form) = 0.3407887692379832 y[1] (numeric) = 0.3407887692379082 absolute error = 7.499556531342932e-14 relative error = 2.200646619931822e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.713 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.713 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.713999999999922 y[1] (closed_form) = 0.3403912320665191 y[1] (numeric) = 0.3403912320664441 absolute error = 7.499556531342932e-14 relative error = 2.203216717955113e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.714 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.714 Order of pole (three term test) = 2.657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.714999999999921 y[1] (closed_form) = 0.3399943900925946 y[1] (numeric) = 0.3399943900925195 absolute error = 7.505107646466058e-14 relative error = 2.207421023747511e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.715 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.715 Order of pole (three term test) = 2.704e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.715999999999921 y[1] (closed_form) = 0.3395982416961749 y[1] (numeric) = 0.3395982416960998 absolute error = 7.510658761589184e-14 relative error = 2.211630638626413e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.716 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.716 Order of pole (three term test) = 5.504e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.716999999999921 y[1] (closed_form) = 0.3392027852619415 y[1] (numeric) = 0.3392027852618663 absolute error = 7.51620987671231e-14 relative error = 2.215845565922488e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.717 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.717 Order of pole (three term test) = 2.801e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.717999999999921 y[1] (closed_form) = 0.3388080191792754 y[1] (numeric) = 0.3388080191792003 absolute error = 7.51620987671231e-14 relative error = 2.218427384015139e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.718 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.718 Order of pole (three term test) = 2.85e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.718999999999921 y[1] (closed_form) = 0.3384139418422416 y[1] (numeric) = 0.3384139418421663 absolute error = 7.521760991835436e-14 relative error = 2.222651038219299e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.719 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.719999999999921 y[1] (closed_form) = 0.3380205516495713 y[1] (numeric) = 0.3380205516494961 absolute error = 7.521760991835436e-14 relative error = 2.225237771824391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.72 Order of pole (three term test) = 2.951e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.720999999999921 y[1] (closed_form) = 0.3376278470046474 y[1] (numeric) = 0.3376278470045722 absolute error = 7.527312106958561e-14 relative error = 2.22947016181842e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.721 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.721 Order of pole (three term test) = 6.006e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.721999999999921 y[1] (closed_form) = 0.3372358263154869 y[1] (numeric) = 0.3372358263154115 absolute error = 7.538414337204813e-14 relative error = 2.235353941948197e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.722 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.722 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.722999999999921 y[1] (closed_form) = 0.3368444879947251 y[1] (numeric) = 0.3368444879946497 absolute error = 7.538414337204813e-14 relative error = 2.237950925687365e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.723 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.723 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72399999999992 y[1] (closed_form) = 0.3364538304596 y[1] (numeric) = 0.3364538304595246 absolute error = 7.543965452327939e-14 relative error = 2.242199306223618e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.724 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.724 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72499999999992 y[1] (closed_form) = 0.3360638521319361 y[1] (numeric) = 0.3360638521318606 absolute error = 7.55506768257419e-14 relative error = 2.248104827295775e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.725 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.725 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72599999999992 y[1] (closed_form) = 0.3356745514381279 y[1] (numeric) = 0.3356745514380524 absolute error = 7.55506768257419e-14 relative error = 2.250712081153031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.726 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.726 Order of pole (three term test) = 6.552e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72699999999992 y[1] (closed_form) = 0.3352859268091249 y[1] (numeric) = 0.3352859268090493 absolute error = 7.560618797697316e-14 relative error = 2.254976482207529e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.727 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.727 Order of pole (three term test) = 6.667e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72799999999992 y[1] (closed_form) = 0.3348979766804151 y[1] (numeric) = 0.3348979766803394 absolute error = 7.566169912820442e-14 relative error = 2.259246230096114e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.728 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.728 Order of pole (three term test) = 3.392e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72899999999992 y[1] (closed_form) = 0.3345106994920096 y[1] (numeric) = 0.3345106994919339 absolute error = 7.566169912820442e-14 relative error = 2.261861855034976e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.729 Order of pole (three term test) = 3.451e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.72999999999992 y[1] (closed_form) = 0.3341240936884268 y[1] (numeric) = 0.3341240936883511 absolute error = 7.571721027943568e-14 relative error = 2.26614038645302e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.73 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.73 Order of pole (three term test) = 3.512e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73099999999992 y[1] (closed_form) = 0.333738157718677 y[1] (numeric) = 0.3337381577186012 absolute error = 7.582823258189819e-14 relative error = 2.272087588073079e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.731 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.731 Order of pole (three term test) = 3.573e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.73199999999992 y[1] (closed_form) = 0.3333528900362464 y[1] (numeric) = 0.3333528900361706 absolute error = 7.582823258189819e-14 relative error = 2.27471351976739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.732 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.732 Order of pole (three term test) = 3.636e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.732999999999919 y[1] (closed_form) = 0.332968289099082 y[1] (numeric) = 0.3329682890990062 absolute error = 7.582823258189819e-14 relative error = 2.277340968026353e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.733 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.733 Order of pole (three term test) = 7.398e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.733999999999919 y[1] (closed_form) = 0.332584353369576 y[1] (numeric) = 0.3325843533695002 absolute error = 7.588374373312945e-14 relative error = 2.281639017720282e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.734 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.734 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.734999999999919 y[1] (closed_form) = 0.3322010813145506 y[1] (numeric) = 0.3322010813144747 absolute error = 7.588374373312945e-14 relative error = 2.284271424790384e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.735 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.735 Order of pole (three term test) = 3.829e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.735999999999919 y[1] (closed_form) = 0.3318184714052423 y[1] (numeric) = 0.3318184714051663 absolute error = 7.593925488436071e-14 relative error = 2.28857828687957e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.736 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.736 Order of pole (three term test) = 3.896e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.736999999999919 y[1] (closed_form) = 0.3314365221172872 y[1] (numeric) = 0.3314365221172111 absolute error = 7.605027718682322e-14 relative error = 2.294565387694688e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.737 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.737 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.737999999999919 y[1] (closed_form) = 0.3310552319307053 y[1] (numeric) = 0.3310552319306292 absolute error = 7.610578833805448e-14 relative error = 2.298884929085928e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.738 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.738 Order of pole (three term test) = 4.033e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.738999999999919 y[1] (closed_form) = 0.3306745993298857 y[1] (numeric) = 0.3306745993298096 absolute error = 7.616129948928574e-14 relative error = 2.303209851728168e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.739 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.739 Order of pole (three term test) = 4.103e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.739999999999919 y[1] (closed_form) = 0.3302946228035716 y[1] (numeric) = 0.3302946228034954 absolute error = 7.616129948928574e-14 relative error = 2.3058595033374e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.74 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.74 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.740999999999919 y[1] (closed_form) = 0.3299153008448449 y[1] (numeric) = 0.3299153008447687 absolute error = 7.6216810640517e-14 relative error = 2.310193266130473e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.741 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.741 Order of pole (three term test) = 4.247e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.741999999999919 y[1] (closed_form) = 0.3295366319511118 y[1] (numeric) = 0.3295366319510355 absolute error = 7.627232179174825e-14 relative error = 2.314532419056331e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.742 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.742 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.742999999999918 y[1] (closed_form) = 0.3291586146240873 y[1] (numeric) = 0.3291586146240109 absolute error = 7.638334409421077e-14 relative error = 2.320563421420512e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.743 Order of pole (three term test) = 8.792e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.743999999999918 y[1] (closed_form) = 0.3287812473697808 y[1] (numeric) = 0.3287812473697044 absolute error = 7.638334409421077e-14 relative error = 2.323226908629077e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.744 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.744 Order of pole (three term test) = 4.472e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.744999999999918 y[1] (closed_form) = 0.3284045286984815 y[1] (numeric) = 0.3284045286984051 absolute error = 7.643885524544203e-14 relative error = 2.327582251937303e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.745 Order of pole (three term test) = 4.55e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.745999999999918 y[1] (closed_form) = 0.3280284571247433 y[1] (numeric) = 0.3280284571246668 absolute error = 7.649436639667329e-14 relative error = 2.33194299870099e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.746 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.746 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.746999999999918 y[1] (closed_form) = 0.32765303116737 y[1] (numeric) = 0.3276530311672935 absolute error = 7.654987754790454e-14 relative error = 2.336309152250807e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.747 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.747 Order of pole (three term test) = 2.354e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.747999999999918 y[1] (closed_form) = 0.3272782493494016 y[1] (numeric) = 0.327278249349325 absolute error = 7.666089985036706e-14 relative error = 2.342376861363739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.748 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.748 Order of pole (three term test) = 2.395e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.748999999999918 y[1] (closed_form) = 0.3269041101980987 y[1] (numeric) = 0.326904110198022 absolute error = 7.666089985036706e-14 relative error = 2.345057693031506e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.749 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.749 Order of pole (three term test) = 4.873e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.749999999999918 y[1] (closed_form) = 0.3265306122449287 y[1] (numeric) = 0.326530612244852 absolute error = 7.677192215282957e-14 relative error = 2.351140115930184e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.75 Order of pole (three term test) = 4.958e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.750999999999918 y[1] (closed_form) = 0.3261577540255513 y[1] (numeric) = 0.3261577540254745 absolute error = 7.682743330406083e-14 relative error = 2.355529873376616e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.751 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.751 Order of pole (three term test) = 7.565e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.751999999999917 y[1] (closed_form) = 0.3257855340798039 y[1] (numeric) = 0.325785534079727 absolute error = 7.682743330406083e-14 relative error = 2.358221138365257e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.752 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.752 Order of pole (three term test) = 5.13e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.752999999999917 y[1] (closed_form) = 0.3254139509516876 y[1] (numeric) = 0.3254139509516107 absolute error = 7.688294445529209e-14 relative error = 2.362619802575904e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.753 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.753 Order of pole (three term test) = 5.219e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.753999999999917 y[1] (closed_form) = 0.3250430031893526 y[1] (numeric) = 0.3250430031892758 absolute error = 7.688294445529209e-14 relative error = 2.36531608743795e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.754 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.754 Order of pole (three term test) = 2.655e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.754999999999917 y[1] (closed_form) = 0.3246726893450847 y[1] (numeric) = 0.3246726893450078 absolute error = 7.693845560652335e-14 relative error = 2.369723667294597e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.755 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.755 Order of pole (three term test) = 2.7e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.755999999999917 y[1] (closed_form) = 0.3243030079752903 y[1] (numeric) = 0.3243030079752133 absolute error = 7.699396675775461e-14 relative error = 2.374136682803171e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.756 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.756 Order of pole (three term test) = 2.747e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.756999999999917 y[1] (closed_form) = 0.3239339576404828 y[1] (numeric) = 0.3239339576404057 absolute error = 7.704947790898586e-14 relative error = 2.378555137294344e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.757 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.757 Order of pole (three term test) = 8.383e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.757999999999917 y[1] (closed_form) = 0.3235655369052687 y[1] (numeric) = 0.3235655369051916 absolute error = 7.710498906021712e-14 relative error = 2.382979034098783e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.758 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.758 Order of pole (three term test) = 2.842e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.758999999999917 y[1] (closed_form) = 0.3231977443383333 y[1] (numeric) = 0.3231977443382562 absolute error = 7.710498906021712e-14 relative error = 2.385690816564031e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.759 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.759 Order of pole (three term test) = 2.891e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.759999999999917 y[1] (closed_form) = 0.3228305785124273 y[1] (numeric) = 0.3228305785123501 absolute error = 7.716050021144838e-14 relative error = 2.390123654549598e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.76 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.76 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.760999999999916 y[1] (closed_form) = 0.3224640380043523 y[1] (numeric) = 0.322464038004275 absolute error = 7.72715225139109e-14 relative error = 2.396283411698391e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.761 Order of pole (three term test) = 5.983e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.761999999999916 y[1] (closed_form) = 0.3220981213949474 y[1] (numeric) = 0.3220981213948701 absolute error = 7.72715225139109e-14 relative error = 2.399005687436556e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.762 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.762 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.762999999999916 y[1] (closed_form) = 0.3217328272690755 y[1] (numeric) = 0.3217328272689982 absolute error = 7.732703366514215e-14 relative error = 2.403454888999284e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.763 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.763 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.763999999999916 y[1] (closed_form) = 0.3213681542156095 y[1] (numeric) = 0.3213681542155321 absolute error = 7.738254481637341e-14 relative error = 2.40790955174907e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.764 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.764 Order of pole (three term test) = 3.148e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.764999999999916 y[1] (closed_form) = 0.3210041008274186 y[1] (numeric) = 0.3210041008273412 absolute error = 7.743805596760467e-14 relative error = 2.412369679016583e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.765 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.765 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.765999999999916 y[1] (closed_form) = 0.3206406657013551 y[1] (numeric) = 0.3206406657012776 absolute error = 7.749356711883593e-14 relative error = 2.416835274132492e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.766 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.766 Order of pole (three term test) = 3.257e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.766999999999916 y[1] (closed_form) = 0.3202778474382401 y[1] (numeric) = 0.3202778474381626 absolute error = 7.749356711883593e-14 relative error = 2.4195731218588e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.767 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.767 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.767999999999916 y[1] (closed_form) = 0.3199156446428511 y[1] (numeric) = 0.3199156446427736 absolute error = 7.754907827006718e-14 relative error = 2.424047700344314e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.768 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.768 Order of pole (three term test) = 3.37e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.768999999999916 y[1] (closed_form) = 0.3195540559239076 y[1] (numeric) = 0.31955405592383 absolute error = 7.760458942129844e-14 relative error = 2.428527755560007e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.769 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.769 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.769999999999915 y[1] (closed_form) = 0.3191930798940584 y[1] (numeric) = 0.3191930798939808 absolute error = 7.760458942129844e-14 relative error = 2.431274181979627e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.77 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.770999999999915 y[1] (closed_form) = 0.3188327151698679 y[1] (numeric) = 0.3188327151697902 absolute error = 7.76601005725297e-14 relative error = 2.435763234997823e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.771 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.771 Order of pole (three term test) = 3.545e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.771999999999915 y[1] (closed_form) = 0.3184729603718031 y[1] (numeric) = 0.3184729603717253 absolute error = 7.771561172376096e-14 relative error = 2.440257773627985e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.772 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.772 Order of pole (three term test) = 7.212e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.772999999999915 y[1] (closed_form) = 0.3181138141242202 y[1] (numeric) = 0.3181138141241424 absolute error = 7.782663402622347e-14 relative error = 2.446502810337968e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.773 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.773 Order of pole (three term test) = 1.1e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.773999999999915 y[1] (closed_form) = 0.3177552750553517 y[1] (numeric) = 0.3177552750552738 absolute error = 7.782663402622347e-14 relative error = 2.449263321046878e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.774 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.774 Order of pole (three term test) = 3.73e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.774999999999915 y[1] (closed_form) = 0.3173973417972929 y[1] (numeric) = 0.3173973417972151 absolute error = 7.782663402622347e-14 relative error = 2.452025388288468e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.775 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.775 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.775999999999915 y[1] (closed_form) = 0.3170400129859893 y[1] (numeric) = 0.3170400129859115 absolute error = 7.782663402622347e-14 relative error = 2.454789012062739e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.776 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.776 Order of pole (three term test) = 3.858e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.776999999999915 y[1] (closed_form) = 0.3166832872612235 y[1] (numeric) = 0.3166832872611456 absolute error = 7.788214517745473e-14 relative error = 2.459307084090354e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.777 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.777 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.777999999999915 y[1] (closed_form) = 0.3163271632666018 y[1] (numeric) = 0.3163271632665239 absolute error = 7.793765632868599e-14 relative error = 2.463830659493501e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.778 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.778999999999914 y[1] (closed_form) = 0.315971639649542 y[1] (numeric) = 0.315971639649464 absolute error = 7.799316747991725e-14 relative error = 2.46835974160285e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.779 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.779 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.779999999999914 y[1] (closed_form) = 0.31561671506126 y[1] (numeric) = 0.315616715061182 absolute error = 7.799316747991725e-14 relative error = 2.47113551843346e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.78 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.780999999999914 y[1] (closed_form) = 0.3152623881567574 y[1] (numeric) = 0.3152623881566793 absolute error = 7.810418978237976e-14 relative error = 2.477434439262832e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.781 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.781 Order of pole (three term test) = 1.259e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.781999999999914 y[1] (closed_form) = 0.3149086575948085 y[1] (numeric) = 0.3149086575947303 absolute error = 7.815970093361102e-14 relative error = 2.481980061474803e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.782 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.782 Order of pole (three term test) = 4.269e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.782999999999914 y[1] (closed_form) = 0.3145555220379475 y[1] (numeric) = 0.3145555220378694 absolute error = 7.815970093361102e-14 relative error = 2.484766454813085e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.783 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.783 Order of pole (three term test) = 4.342e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.783999999999914 y[1] (closed_form) = 0.3142029801524565 y[1] (numeric) = 0.3142029801523783 absolute error = 7.815970093361102e-14 relative error = 2.487554411345387e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.784 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.784 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.784999999999914 y[1] (closed_form) = 0.3138510306083521 y[1] (numeric) = 0.3138510306082739 absolute error = 7.827072323607354e-14 relative error = 2.493881351428343e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.785 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.785 Order of pole (three term test) = 4.49e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.785999999999914 y[1] (closed_form) = 0.3134996720793733 y[1] (numeric) = 0.313499672079295 absolute error = 7.827072323607354e-14 relative error = 2.496676398955103e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.786 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.786999999999914 y[1] (closed_form) = 0.313148903242969 y[1] (numeric) = 0.3131489032428907 absolute error = 7.832623438730479e-14 relative error = 2.501245687791289e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.787 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.787 Order of pole (three term test) = 1.161e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.787999999999913 y[1] (closed_form) = 0.3127987227802854 y[1] (numeric) = 0.312798722780207 absolute error = 7.838174553853605e-14 relative error = 2.505820511089253e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.788 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.788 Order of pole (three term test) = 4.722e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.788999999999913 y[1] (closed_form) = 0.3124491293761538 y[1] (numeric) = 0.3124491293760753 absolute error = 7.849276784099857e-14 relative error = 2.512177518232162e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.789 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.789 Order of pole (three term test) = 4.802e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.789999999999913 y[1] (closed_form) = 0.3121001217190777 y[1] (numeric) = 0.3121001217189993 absolute error = 7.843725668976731e-14 relative error = 2.513208141596591e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.79 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.79 Order of pole (three term test) = 4.883e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.790999999999913 y[1] (closed_form) = 0.3117516985012216 y[1] (numeric) = 0.3117516985011431 absolute error = 7.849276784099857e-14 relative error = 2.517797600409577e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.791 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.791 Order of pole (three term test) = 2.483e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.791999999999913 y[1] (closed_form) = 0.3114038584183976 y[1] (numeric) = 0.311403858418319 absolute error = 7.854827899222983e-14 relative error = 2.522392605896794e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.792 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.792 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.792999999999913 y[1] (closed_form) = 0.3110566001700538 y[1] (numeric) = 0.3110566001699752 absolute error = 7.860379014346108e-14 relative error = 2.526993161388912e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.793 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.793 Order of pole (three term test) = 5.135e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.793999999999913 y[1] (closed_form) = 0.3107099224592619 y[1] (numeric) = 0.3107099224591833 absolute error = 7.860379014346108e-14 relative error = 2.529812679341357e-11 % Desired digits = 8 Estimated correct digits = 12 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.794 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.794 Order of pole (three term test) = 5.221e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.794999999999913 y[1] (closed_form) = 0.3103638239927056 y[1] (numeric) = 0.310363823992627 absolute error = 7.865930129469234e-14 relative error = 2.534422352540064e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.795 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.795 Order of pole (three term test) = 2.655e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.795999999999913 y[1] (closed_form) = 0.3100183034806677 y[1] (numeric) = 0.310018303480589 absolute error = 7.865930129469234e-14 relative error = 2.537247008049556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.796 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.796 Order of pole (three term test) = 5.399e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.796999999999912 y[1] (closed_form) = 0.3096733596370187 y[1] (numeric) = 0.30967335963694 absolute error = 7.87148124459236e-14 relative error = 2.541865807836637e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.797 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.797 Order of pole (three term test) = 5.49e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.797999999999912 y[1] (closed_form) = 0.3093289911792047 y[1] (numeric) = 0.3093289911791259 absolute error = 7.877032359715486e-14 relative error = 2.546490172061517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.798 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.798 Order of pole (three term test) = 5.582e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.798999999999912 y[1] (closed_form) = 0.3089851968282353 y[1] (numeric) = 0.3089851968281566 absolute error = 7.877032359715486e-14 relative error = 2.549323540601307e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.799 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.799 Order of pole (three term test) = 2.838e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.799999999999912 y[1] (closed_form) = 0.3086419753086721 y[1] (numeric) = 0.3086419753085933 absolute error = 7.877032359715486e-14 relative error = 2.552158484547568e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.8 Order of pole (three term test) = 5.771e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.800999999999912 y[1] (closed_form) = 0.3082993253486165 y[1] (numeric) = 0.3082993253485377 absolute error = 7.882583474838611e-14 relative error = 2.556795564156749e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.801 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.801 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.801999999999912 y[1] (closed_form) = 0.307957245679698 y[1] (numeric) = 0.3079572456796191 absolute error = 7.888134589961737e-14 relative error = 2.56143821930596e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.802 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.802 Order of pole (three term test) = 2.983e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.802999999999912 y[1] (closed_form) = 0.3076157350370624 y[1] (numeric) = 0.3076157350369835 absolute error = 7.888134589961737e-14 relative error = 2.564281891825642e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.803 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.803 Order of pole (three term test) = 6.067e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.803999999999912 y[1] (closed_form) = 0.3072747921593607 y[1] (numeric) = 0.3072747921592817 absolute error = 7.893685705084863e-14 relative error = 2.568933705759694e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.804 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.804 Order of pole (three term test) = 6.169e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.804999999999912 y[1] (closed_form) = 0.3069344157887364 y[1] (numeric) = 0.3069344157886574 absolute error = 7.899236820207989e-14 relative error = 2.573591104115561e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.805 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.805 Order of pole (three term test) = 6.272e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.805999999999911 y[1] (closed_form) = 0.306594604670815 y[1] (numeric) = 0.3065946046707359 absolute error = 7.904787935331115e-14 relative error = 2.57825409022391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.806 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.806 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.806999999999911 y[1] (closed_form) = 0.3062553575546912 y[1] (numeric) = 0.3062553575546123 absolute error = 7.899236820207989e-14 relative error = 2.579297512794479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.807 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.807 Order of pole (three term test) = 9.726e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.807999999999911 y[1] (closed_form) = 0.3059166731929191 y[1] (numeric) = 0.30591667319284 absolute error = 7.91033905045424e-14 relative error = 2.585782254982151e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.808 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.808 Order of pole (three term test) = 3.296e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.808999999999911 y[1] (closed_form) = 0.3055785503414988 y[1] (numeric) = 0.3055785503414197 absolute error = 7.91033905045424e-14 relative error = 2.5886434246167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.809 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.809 Order of pole (three term test) = 3.351e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.809999999999911 y[1] (closed_form) = 0.3052409877598664 y[1] (numeric) = 0.3052409877597873 absolute error = 7.91033905045424e-14 relative error = 2.591506176319059e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.81 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.81 Order of pole (three term test) = 6.815e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.810999999999911 y[1] (closed_form) = 0.3049039842108821 y[1] (numeric) = 0.3049039842108029 absolute error = 7.921441280700492e-14 relative error = 2.598011731857774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.811 Order of pole (three term test) = 3.464e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.811999999999911 y[1] (closed_form) = 0.3045675384608187 y[1] (numeric) = 0.3045675384607395 absolute error = 7.921441280700492e-14 relative error = 2.600881670033771e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.812 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.812 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.812999999999911 y[1] (closed_form) = 0.3042316492793508 y[1] (numeric) = 0.3042316492792716 absolute error = 7.921441280700492e-14 relative error = 2.603753192498025e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.813 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.813 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.813999999999911 y[1] (closed_form) = 0.303896315439543 y[1] (numeric) = 0.3038963154394638 absolute error = 7.926992395823618e-14 relative error = 2.608452946972504e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.814 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.814 Order of pole (three term test) = 3.641e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81499999999991 y[1] (closed_form) = 0.3035615357178392 y[1] (numeric) = 0.3035615357177598 absolute error = 7.932543510946743e-14 relative error = 2.613158314734595e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.815 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.815 Order of pole (three term test) = 3.701e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81599999999991 y[1] (closed_form) = 0.3032273088940508 y[1] (numeric) = 0.3032273088939714 absolute error = 7.932543510946743e-14 relative error = 2.61603862128342e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.816 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.816 Order of pole (three term test) = 3.763e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81699999999991 y[1] (closed_form) = 0.3028936337513464 y[1] (numeric) = 0.302893633751267 absolute error = 7.938094626069869e-14 relative error = 2.62075320889262e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.817 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.817 Order of pole (three term test) = 7.652e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81799999999991 y[1] (closed_form) = 0.3025605090762401 y[1] (numeric) = 0.3025605090761607 absolute error = 7.943645741192995e-14 relative error = 2.625473418671216e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.818 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.818 Order of pole (three term test) = 3.889e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81899999999991 y[1] (closed_form) = 0.3022279336585806 y[1] (numeric) = 0.3022279336585012 absolute error = 7.943645741192995e-14 relative error = 2.628362522627288e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.819 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.819 Order of pole (three term test) = 3.954e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.81999999999991 y[1] (closed_form) = 0.3018959062915406 y[1] (numeric) = 0.3018959062914611 absolute error = 7.949196856316121e-14 relative error = 2.633091966685891e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.82 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82099999999991 y[1] (closed_form) = 0.3015644257716051 y[1] (numeric) = 0.3015644257715256 absolute error = 7.949196856316121e-14 relative error = 2.635986269261276e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.821 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.821 Order of pole (three term test) = 4.087e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82199999999991 y[1] (closed_form) = 0.3012334908985612 y[1] (numeric) = 0.3012334908984817 absolute error = 7.954747971439247e-14 relative error = 2.64072495648167e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.822 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.822 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.82299999999991 y[1] (closed_form) = 0.3009031004754868 y[1] (numeric) = 0.3009031004754073 absolute error = 7.949196856316121e-14 relative error = 2.641779643930158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.823 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.823 Order of pole (three term test) = 4.224e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.823999999999909 y[1] (closed_form) = 0.3005732533087402 y[1] (numeric) = 0.3005732533086606 absolute error = 7.960299086562372e-14 relative error = 2.64837240138123e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.824 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.824 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.824999999999909 y[1] (closed_form) = 0.3002439482079488 y[1] (numeric) = 0.3002439482078691 absolute error = 7.960299086562372e-14 relative error = 2.651277114517917e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.825 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.825 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.825999999999909 y[1] (closed_form) = 0.2999151839859986 y[1] (numeric) = 0.2999151839859189 absolute error = 7.965850201685498e-14 relative error = 2.656034314707247e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.826 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.826 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.826999999999909 y[1] (closed_form) = 0.2995869594590237 y[1] (numeric) = 0.299586959458944 absolute error = 7.971401316808624e-14 relative error = 2.660797162601104e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.827 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.827 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.827999999999909 y[1] (closed_form) = 0.2992592734463954 y[1] (numeric) = 0.2992592734463156 absolute error = 7.97695243193175e-14 relative error = 2.665565661530157e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.828 Order of pole (three term test) = 4.585e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.828999999999909 y[1] (closed_form) = 0.2989321247707115 y[1] (numeric) = 0.2989321247706317 absolute error = 7.97695243193175e-14 relative error = 2.668482833034514e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.829 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.829 Order of pole (three term test) = 2.331e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.829999999999909 y[1] (closed_form) = 0.298605512257786 y[1] (numeric) = 0.2986055122577062 absolute error = 7.982503547054876e-14 relative error = 2.673260612872941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.83 Order of pole (three term test) = 2.369e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.830999999999909 y[1] (closed_form) = 0.2982794347366385 y[1] (numeric) = 0.2982794347365587 absolute error = 7.982503547054876e-14 relative error = 2.676183007421517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.831 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.831 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.831999999999909 y[1] (closed_form) = 0.2979538910394836 y[1] (numeric) = 0.2979538910394037 absolute error = 7.988054662178001e-14 relative error = 2.680970077051102e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.832 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.832 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.832999999999908 y[1] (closed_form) = 0.2976288800017202 y[1] (numeric) = 0.2976288800016403 absolute error = 7.988054662178001e-14 relative error = 2.68389769908479e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.833 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.833 Order of pole (three term test) = 2.488e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.833999999999908 y[1] (closed_form) = 0.2973044004619219 y[1] (numeric) = 0.2973044004618419 absolute error = 7.999156892424253e-14 relative error = 2.690561216045226e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.834 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.834 Order of pole (three term test) = 1.012e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.834999999999908 y[1] (closed_form) = 0.2969804512618254 y[1] (numeric) = 0.2969804512617454 absolute error = 7.999156892424253e-14 relative error = 2.693496106709056e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.835 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.835999999999908 y[1] (closed_form) = 0.2966570312463215 y[1] (numeric) = 0.2966570312462414 absolute error = 8.004708007547379e-14 relative error = 2.698303820380673e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.836 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.836999999999908 y[1] (closed_form) = 0.2963341392634438 y[1] (numeric) = 0.2963341392633637 absolute error = 8.010259122670504e-14 relative error = 2.703117211732837e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.837 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.837 Order of pole (three term test) = 2.657e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.837999999999908 y[1] (closed_form) = 0.2960117741643589 y[1] (numeric) = 0.2960117741642787 absolute error = 8.01581023779363e-14 relative error = 2.707936284096219e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.838 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.838 Order of pole (three term test) = 2.7e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.838999999999908 y[1] (closed_form) = 0.2956899348033559 y[1] (numeric) = 0.2956899348032758 absolute error = 8.01581023779363e-14 relative error = 2.710883697520655e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.839 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.839 Order of pole (three term test) = 5.489e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.839999999999908 y[1] (closed_form) = 0.2953686200378368 y[1] (numeric) = 0.2953686200377566 absolute error = 8.021361352916756e-14 relative error = 2.715712099643225e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.84 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.840999999999908 y[1] (closed_form) = 0.2950478287283056 y[1] (numeric) = 0.2950478287282254 absolute error = 8.026912468039882e-14 relative error = 2.720546191658794e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.841 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.841 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.841999999999907 y[1] (closed_form) = 0.2947275597383587 y[1] (numeric) = 0.2947275597382784 absolute error = 8.026912468039882e-14 relative error = 2.723502503520774e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.842 Order of pole (three term test) = 2.882e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.842999999999907 y[1] (closed_form) = 0.2944078119346746 y[1] (numeric) = 0.2944078119345943 absolute error = 8.032463583163008e-14 relative error = 2.728345939728431e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.843 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.843 Order of pole (three term test) = 2.93e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.843999999999907 y[1] (closed_form) = 0.294088584187004 y[1] (numeric) = 0.2940885841869237 absolute error = 8.032463583163008e-14 relative error = 2.731307509051542e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.844 Order of pole (three term test) = 5.955e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.844999999999907 y[1] (closed_form) = 0.29376987536816 y[1] (numeric) = 0.2937698753680795 absolute error = 8.043565813409259e-14 relative error = 2.73804991179877e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.845 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.845 Order of pole (three term test) = 6.053e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.845999999999907 y[1] (closed_form) = 0.2934516843540074 y[1] (numeric) = 0.2934516843539269 absolute error = 8.049116928532385e-14 relative error = 2.74291045432279e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.846 Order of pole (three term test) = 6.152e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.846999999999907 y[1] (closed_form) = 0.2931340100234539 y[1] (numeric) = 0.2931340100233734 absolute error = 8.049116928532385e-14 relative error = 2.745882993204497e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.847 Order of pole (three term test) = 3.126e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.847999999999907 y[1] (closed_form) = 0.2928168512584393 y[1] (numeric) = 0.2928168512583587 absolute error = 8.060219158778636e-14 relative error = 2.752648669001878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.848 Order of pole (three term test) = 3.178e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.848999999999907 y[1] (closed_form) = 0.2925002069439259 y[1] (numeric) = 0.2925002069438453 absolute error = 8.060219158778636e-14 relative error = 2.755628532024878e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.849 Order of pole (three term test) = 6.459e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.849999999999907 y[1] (closed_form) = 0.2921840759678893 y[1] (numeric) = 0.2921840759678086 absolute error = 8.065770273901762e-14 relative error = 2.760509876242599e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 Order of pole (three term test) = 3.282e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.850999999999906 y[1] (closed_form) = 0.2918684572213075 y[1] (numeric) = 0.2918684572212268 absolute error = 8.065770273901762e-14 relative error = 2.76349501782097e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.851 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.851 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.851999999999906 y[1] (closed_form) = 0.2915533495981523 y[1] (numeric) = 0.2915533495980716 absolute error = 8.071321389024888e-14 relative error = 2.768385751749922e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.852 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.852 Order of pole (three term test) = 3.391e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.852999999999906 y[1] (closed_form) = 0.2912387519953789 y[1] (numeric) = 0.2912387519952982 absolute error = 8.071321389024888e-14 relative error = 2.771376176324556e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.853 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.853 Order of pole (three term test) = 3.446e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.853999999999906 y[1] (closed_form) = 0.2909246633129166 y[1] (numeric) = 0.2909246633128358 absolute error = 8.08242361927114e-14 relative error = 2.778184402529578e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.854 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.854 Order of pole (three term test) = 3.502e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.854999999999906 y[1] (closed_form) = 0.2906110824536588 y[1] (numeric) = 0.290611082453578 absolute error = 8.08242361927114e-14 relative error = 2.781182173449966e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.855 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.855 Order of pole (three term test) = 3.559e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.855999999999906 y[1] (closed_form) = 0.2902980083234539 y[1] (numeric) = 0.290298008323373 absolute error = 8.08242361927114e-14 relative error = 2.784181560855077e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.856 Order of pole (three term test) = 7.235e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.856999999999906 y[1] (closed_form) = 0.2899854398310955 y[1] (numeric) = 0.2899854398310146 absolute error = 8.093525849517391e-14 relative error = 2.791011112223956e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.857 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.857 Order of pole (three term test) = 3.676e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.857999999999906 y[1] (closed_form) = 0.2896733758883128 y[1] (numeric) = 0.2896733758882319 absolute error = 8.093525849517391e-14 relative error = 2.794017857077052e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.858 Order of pole (three term test) = 1.121e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.858999999999906 y[1] (closed_form) = 0.2893618154097614 y[1] (numeric) = 0.2893618154096804 absolute error = 8.099076964640517e-14 relative error = 2.798944619963599e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.859 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.859 Order of pole (three term test) = 3.797e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.859999999999906 y[1] (closed_form) = 0.2890507573130135 y[1] (numeric) = 0.2890507573129326 absolute error = 8.093525849517391e-14 relative error = 2.800036202898753e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.86 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.86 Order of pole (three term test) = 3.859e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.860999999999905 y[1] (closed_form) = 0.288740200518549 y[1] (numeric) = 0.288740200518468 absolute error = 8.099076964640517e-14 relative error = 2.804970333225291e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.861 Order of pole (three term test) = 3.921e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.861999999999905 y[1] (closed_form) = 0.2884301439497456 y[1] (numeric) = 0.2884301439496645 absolute error = 8.104628079763643e-14 relative error = 2.80991021561732e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.862 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.862999999999905 y[1] (closed_form) = 0.2881205865328698 y[1] (numeric) = 0.2881205865327887 absolute error = 8.110179194886769e-14 relative error = 2.814855853405509e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.863 Order of pole (three term test) = 4.05e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.863999999999905 y[1] (closed_form) = 0.2878115271970674 y[1] (numeric) = 0.2878115271969863 absolute error = 8.110179194886769e-14 relative error = 2.817878517191443e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.864 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.864999999999905 y[1] (closed_form) = 0.2875029648743546 y[1] (numeric) = 0.2875029648742734 absolute error = 8.115730310009894e-14 relative error = 2.822833605753129e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.865 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.865 Order of pole (three term test) = 4.182e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.865999999999905 y[1] (closed_form) = 0.2871948984996083 y[1] (numeric) = 0.2871948984995271 absolute error = 8.12128142513302e-14 relative error = 2.827794458592758e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.866 Order of pole (three term test) = 8.5e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.866999999999905 y[1] (closed_form) = 0.2868873270105572 y[1] (numeric) = 0.2868873270104759 absolute error = 8.126832540256146e-14 relative error = 2.832761079041001e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.867 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.867 Order of pole (three term test) = 4.319e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.867999999999905 y[1] (closed_form) = 0.2865802493477727 y[1] (numeric) = 0.2865802493476913 absolute error = 8.132383655379272e-14 relative error = 2.837733470428526e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.868 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.868999999999905 y[1] (closed_form) = 0.2862736644546593 y[1] (numeric) = 0.286273664454578 absolute error = 8.137934770502397e-14 relative error = 2.842711636086002e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.869 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.869 Order of pole (three term test) = 4.46e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.869999999999904 y[1] (closed_form) = 0.2859675712774464 y[1] (numeric) = 0.285967571277365 absolute error = 8.137934770502397e-14 relative error = 2.845754409896692e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.87 Order of pole (three term test) = 9.064e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.870999999999904 y[1] (closed_form) = 0.2856619687651782 y[1] (numeric) = 0.2856619687650968 absolute error = 8.143485885625523e-14 relative error = 2.85074205741391e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.871 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.871 Order of pole (three term test) = 4.605e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.871999999999904 y[1] (closed_form) = 0.2853568558697056 y[1] (numeric) = 0.2853568558696241 absolute error = 8.143485885625523e-14 relative error = 2.8537901641809e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.872 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.872 Order of pole (three term test) = 2.34e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.872999999999904 y[1] (closed_form) = 0.2850522315456764 y[1] (numeric) = 0.2850522315455949 absolute error = 8.149037000748649e-14 relative error = 2.858787302439643e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.873 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.873 Order of pole (three term test) = 4.755e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.873999999999904 y[1] (closed_form) = 0.2847480947505272 y[1] (numeric) = 0.2847480947504457 absolute error = 8.154588115871775e-14 relative error = 2.863790229401237e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.874 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.874 Order of pole (three term test) = 4.832e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.874999999999904 y[1] (closed_form) = 0.2844444444444736 y[1] (numeric) = 0.284444444444392 absolute error = 8.154588115871775e-14 relative error = 2.866847384485877e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.875 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.875 Order of pole (three term test) = 4.91e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.875999999999904 y[1] (closed_form) = 0.284141279590502 y[1] (numeric) = 0.2841412795904204 absolute error = 8.160139230994901e-14 relative error = 2.871859816621896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.876 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.876 Order of pole (three term test) = 2.495e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.876999999999904 y[1] (closed_form) = 0.2838385991543604 y[1] (numeric) = 0.2838385991542788 absolute error = 8.165690346118026e-14 relative error = 2.87687804634255e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.877 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.877 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.877999999999904 y[1] (closed_form) = 0.2835364021045497 y[1] (numeric) = 0.2835364021044681 absolute error = 8.165690346118026e-14 relative error = 2.879944263067517e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.878 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.878 Order of pole (three term test) = 2.576e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.878999999999903 y[1] (closed_form) = 0.2832346874123148 y[1] (numeric) = 0.2832346874122332 absolute error = 8.165690346118026e-14 relative error = 2.883012112930554e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.879 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.879 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.879999999999903 y[1] (closed_form) = 0.2829334540516362 y[1] (numeric) = 0.2829334540515545 absolute error = 8.171241461241152e-14 relative error = 2.888043582060776e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.88 Order of pole (three term test) = 2.659e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.880999999999903 y[1] (closed_form) = 0.2826327009992204 y[1] (numeric) = 0.2826327009991387 absolute error = 8.171241461241152e-14 relative error = 2.891116785974348e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.881 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.881 Order of pole (three term test) = 2.702e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.881999999999903 y[1] (closed_form) = 0.2823324272344926 y[1] (numeric) = 0.2823324272344108 absolute error = 8.176792576364278e-14 relative error = 2.896157786924349e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.882 Order of pole (three term test) = 2.745e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.882999999999903 y[1] (closed_form) = 0.2820326317395866 y[1] (numeric) = 0.2820326317395048 absolute error = 8.187894806610529e-14 relative error = 2.903172854895308e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.883 Order of pole (three term test) = 2.789e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.883999999999903 y[1] (closed_form) = 0.2817333134993372 y[1] (numeric) = 0.2817333134992552 absolute error = 8.193445921733655e-14 relative error = 2.908227578757005e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.884 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.884 Order of pole (three term test) = 5.669e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.884999999999903 y[1] (closed_form) = 0.2814344715012709 y[1] (numeric) = 0.2814344715011889 absolute error = 8.193445921733655e-14 relative error = 2.911315688524906e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.885 Order of pole (three term test) = 2.88e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.885999999999903 y[1] (closed_form) = 0.281136104735598 y[1] (numeric) = 0.2811361047355161 absolute error = 8.193445921733655e-14 relative error = 2.914405436981992e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.886 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.886 Order of pole (three term test) = 2.926e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.886999999999903 y[1] (closed_form) = 0.2808382121952037 y[1] (numeric) = 0.2808382121951217 absolute error = 8.193445921733655e-14 relative error = 2.917496824128262e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.887 Order of pole (three term test) = 2.973e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.887999999999902 y[1] (closed_form) = 0.2805407928756394 y[1] (numeric) = 0.2805407928755574 absolute error = 8.198997036856781e-14 relative error = 2.92256856937426e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.888 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.888 Order of pole (three term test) = 3.02e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.888999999999902 y[1] (closed_form) = 0.2802438457751148 y[1] (numeric) = 0.2802438457750328 absolute error = 8.204548151979907e-14 relative error = 2.927646146621806e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.889 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.889 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.889999999999902 y[1] (closed_form) = 0.2799473698944888 y[1] (numeric) = 0.2799473698944067 absolute error = 8.210099267103033e-14 relative error = 2.932729559201571e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.89 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.89 Order of pole (three term test) = 3.118e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.890999999999902 y[1] (closed_form) = 0.2796513642372617 y[1] (numeric) = 0.2796513642371796 absolute error = 8.215650382226158e-14 relative error = 2.937818810444221e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.891 Order of pole (three term test) = 3.168e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.891999999999902 y[1] (closed_form) = 0.2793558278095664 y[1] (numeric) = 0.2793558278094842 absolute error = 8.221201497349284e-14 relative error = 2.942913903680427e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.892 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.892 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.892999999999902 y[1] (closed_form) = 0.2790607596201602 y[1] (numeric) = 0.279060759620078 absolute error = 8.221201497349284e-14 relative error = 2.946025628447174e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.893 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.893 Order of pole (three term test) = 3.27e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.893999999999902 y[1] (closed_form) = 0.2787661586804168 y[1] (numeric) = 0.2787661586803346 absolute error = 8.22675261247241e-14 relative error = 2.951130313455202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.894 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.894 Order of pole (three term test) = 3.322e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.894999999999902 y[1] (closed_form) = 0.2784720240043174 y[1] (numeric) = 0.278472024004235 absolute error = 8.237854842718662e-14 relative error = 2.95823426865707e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.895 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.895999999999902 y[1] (closed_form) = 0.2781783546084428 y[1] (numeric) = 0.2781783546083604 absolute error = 8.237854842718662e-14 relative error = 2.961357239427945e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.896 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.896 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.896999999999901 y[1] (closed_form) = 0.2778851495119653 y[1] (numeric) = 0.2778851495118829 absolute error = 8.237854842718662e-14 relative error = 2.964481857769788e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.897 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.897 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.897999999999901 y[1] (closed_form) = 0.2775924077366403 y[1] (numeric) = 0.2775924077365579 absolute error = 8.243405957841787e-14 relative error = 2.969607859614999e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.898 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.898 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.898999999999901 y[1] (closed_form) = 0.2773001283067982 y[1] (numeric) = 0.2773001283067158 absolute error = 8.243405957841787e-14 relative error = 2.972737880857191e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.899 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.899 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.899999999999901 y[1] (closed_form) = 0.2770083102493363 y[1] (numeric) = 0.2770083102492539 absolute error = 8.243405957841787e-14 relative error = 2.975869550780576e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.9 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.9 Order of pole (three term test) = 3.653e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900999999999901 y[1] (closed_form) = 0.2767169525937107 y[1] (numeric) = 0.2767169525936282 absolute error = 8.248957072964913e-14 relative error = 2.981008931923457e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.901 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.901 Order of pole (three term test) = 7.422e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.901999999999901 y[1] (closed_form) = 0.276426054371928 y[1] (numeric) = 0.2764260543718455 absolute error = 8.248957072964913e-14 relative error = 2.984146010298306e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.902 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.902 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.902999999999901 y[1] (closed_form) = 0.2761356146185378 y[1] (numeric) = 0.2761356146184552 absolute error = 8.254508188088039e-14 relative error = 2.98929502429126e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.903 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.903 Order of pole (three term test) = 3.83e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.903999999999901 y[1] (closed_form) = 0.2758456323706241 y[1] (numeric) = 0.2758456323705415 absolute error = 8.260059303211165e-14 relative error = 2.994449914694684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.904 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.904999999999901 y[1] (closed_form) = 0.2755561066677977 y[1] (numeric) = 0.275556106667715 absolute error = 8.26561041833429e-14 relative error = 2.999610684839246e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.905 Order of pole (three term test) = 7.905e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9059999999999 y[1] (closed_form) = 0.275267036552188 y[1] (numeric) = 0.2752670365521053 absolute error = 8.26561041833429e-14 relative error = 3.002760708969674e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.906 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.906 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9069999999999 y[1] (closed_form) = 0.2749784210684354 y[1] (numeric) = 0.2749784210683527 absolute error = 8.271161533457416e-14 relative error = 3.007931131948324e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.907 Order of pole (three term test) = 8.158e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9079999999999 y[1] (closed_form) = 0.2746902592636831 y[1] (numeric) = 0.2746902592636003 absolute error = 8.276712648580542e-14 relative error = 3.013107443549896e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.908 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.908 Order of pole (three term test) = 4.143e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9089999999999 y[1] (closed_form) = 0.2744025501875691 y[1] (numeric) = 0.2744025501874864 absolute error = 8.271161533457416e-14 relative error = 3.014243682430658e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.909 Order of pole (three term test) = 8.418e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9099999999999 y[1] (closed_form) = 0.2741152928922191 y[1] (numeric) = 0.2741152928921364 absolute error = 8.276712648580542e-14 relative error = 3.019427541328351e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.91 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.91 Order of pole (three term test) = 4.276e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9109999999999 y[1] (closed_form) = 0.2738284864322379 y[1] (numeric) = 0.2738284864321551 absolute error = 8.276712648580542e-14 relative error = 3.022590073231374e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.911 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.911 Order of pole (three term test) = 4.343e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9119999999999 y[1] (closed_form) = 0.2735421298647019 y[1] (numeric) = 0.2735421298646191 absolute error = 8.282263763703668e-14 relative error = 3.027783606057393e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.912 Order of pole (three term test) = 4.412e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9129999999999 y[1] (closed_form) = 0.2732562222491515 y[1] (numeric) = 0.2732562222490685 absolute error = 8.293365993949919e-14 relative error = 3.035014509711013e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.913 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.913 Order of pole (three term test) = 4.482e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.9139999999999 y[1] (closed_form) = 0.272970762647583 y[1] (numeric) = 0.2729707626475 absolute error = 8.293365993949919e-14 relative error = 3.038188380876897e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.914 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.914 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.914999999999899 y[1] (closed_form) = 0.2726857501244415 y[1] (numeric) = 0.2726857501243585 absolute error = 8.293365993949919e-14 relative error = 3.04136391071598e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.915 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.915 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.915999999999899 y[1] (closed_form) = 0.2724011837466128 y[1] (numeric) = 0.2724011837465297 absolute error = 8.304468224196171e-14 relative error = 3.048616790124149e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.916 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.916 Order of pole (three term test) = 7.046e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.916999999999899 y[1] (closed_form) = 0.2721170625834155 y[1] (numeric) = 0.2721170625833325 absolute error = 8.304468224196171e-14 relative error = 3.051799892794483e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.917 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.917 Order of pole (three term test) = 2.386e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.917999999999899 y[1] (closed_form) = 0.2718333857065943 y[1] (numeric) = 0.2718333857065112 absolute error = 8.310019339319297e-14 relative error = 3.057026758401482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.918 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.918 Order of pole (three term test) = 2.423e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.918999999999899 y[1] (closed_form) = 0.2715501521903114 y[1] (numeric) = 0.2715501521902283 absolute error = 8.310019339319297e-14 relative error = 3.060215312821979e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.919 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.919 Order of pole (three term test) = 2.462e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.919999999999899 y[1] (closed_form) = 0.2712673611111397 y[1] (numeric) = 0.2712673611110565 absolute error = 8.315570454442422e-14 relative error = 3.065451892325331e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.92 Order of pole (three term test) = 2.5e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.920999999999899 y[1] (closed_form) = 0.2709850115480548 y[1] (numeric) = 0.2709850115479717 absolute error = 8.315570454442422e-14 relative error = 3.068645902936883e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.921 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.921 Order of pole (three term test) = 5.08e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.921999999999899 y[1] (closed_form) = 0.2707031025824279 y[1] (numeric) = 0.2707031025823446 absolute error = 8.326672684688674e-14 relative error = 3.075942833774222e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.922 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.922 Order of pole (three term test) = 2.58e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.922999999999899 y[1] (closed_form) = 0.2704216332980178 y[1] (numeric) = 0.2704216332979345 absolute error = 8.326672684688674e-14 relative error = 3.079144439421485e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.923 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.923 Order of pole (three term test) = 2.62e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.923999999999898 y[1] (closed_form) = 0.270140602780964 y[1] (numeric) = 0.2701406027808806 absolute error = 8.3322237998118e-14 relative error = 3.084402608876887e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.924 Order of pole (three term test) = 7.985e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.924999999999898 y[1] (closed_form) = 0.2698600101197789 y[1] (numeric) = 0.2698600101196956 absolute error = 8.3322237998118e-14 relative error = 3.087609681817434e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.925 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.925 Order of pole (three term test) = 8.11e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.925999999999898 y[1] (closed_form) = 0.2695798544053407 y[1] (numeric) = 0.2695798544052574 absolute error = 8.3322237998118e-14 relative error = 3.090818421202741e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.926 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.926999999999898 y[1] (closed_form) = 0.2693001347308859 y[1] (numeric) = 0.2693001347308025 absolute error = 8.337774914934926e-14 relative error = 3.096090138709712e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.927 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.927 Order of pole (three term test) = 2.789e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.927999999999898 y[1] (closed_form) = 0.2690208501920018 y[1] (numeric) = 0.2690208501919183 absolute error = 8.343326030058051e-14 relative error = 3.101367802571202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.928 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.928 Order of pole (three term test) = 5.665e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.928999999999898 y[1] (closed_form) = 0.2687419998866193 y[1] (numeric) = 0.2687419998865359 absolute error = 8.343326030058051e-14 relative error = 3.104585823420995e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.929 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.929 Order of pole (three term test) = 5.754e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.929999999999898 y[1] (closed_form) = 0.268463582915006 y[1] (numeric) = 0.2684635829149226 absolute error = 8.348877145181177e-14 relative error = 3.109873247808207e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.93 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.93 Order of pole (three term test) = 5.844e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.930999999999898 y[1] (closed_form) = 0.2681855983797584 y[1] (numeric) = 0.2681855983796748 absolute error = 8.354428260304303e-14 relative error = 3.115166627431722e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.931 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.931 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.931999999999898 y[1] (closed_form) = 0.2679080453857945 y[1] (numeric) = 0.2679080453857111 absolute error = 8.348877145181177e-14 relative error = 3.116321920515144e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.932 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.932999999999897 y[1] (closed_form) = 0.2676309230403478 y[1] (numeric) = 0.2676309230402643 absolute error = 8.354428260304303e-14 relative error = 3.121622929591285e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.933 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.933 Order of pole (three term test) = 6.123e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.933999999999897 y[1] (closed_form) = 0.2673542304529585 y[1] (numeric) = 0.267354230452875 absolute error = 8.354428260304303e-14 relative error = 3.124853586999545e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.934 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.934 Order of pole (three term test) = 9.328e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.934999999999897 y[1] (closed_form) = 0.2670779667354676 y[1] (numeric) = 0.267077966735384 absolute error = 8.359979375427429e-14 relative error = 3.130164377695644e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.935 Order of pole (three term test) = 3.158e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.935999999999897 y[1] (closed_form) = 0.2668021310020091 y[1] (numeric) = 0.2668021310019255 absolute error = 8.365530490550555e-14 relative error = 3.135481136950724e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.936 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.936 Order of pole (three term test) = 3.207e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.936999999999897 y[1] (closed_form) = 0.2665267223690032 y[1] (numeric) = 0.2665267223689194 absolute error = 8.37108160567368e-14 relative error = 3.140803868095453e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.937 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.937 Order of pole (three term test) = 9.772e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.937999999999897 y[1] (closed_form) = 0.2662517399551489 y[1] (numeric) = 0.2662517399550652 absolute error = 8.37108160567368e-14 relative error = 3.144047662217651e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.938 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.938999999999897 y[1] (closed_form) = 0.2659771828814176 y[1] (numeric) = 0.2659771828813339 absolute error = 8.37108160567368e-14 relative error = 3.147293130556171e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.939 Order of pole (three term test) = 3.36e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.939999999999897 y[1] (closed_form) = 0.2657030502710454 y[1] (numeric) = 0.2657030502709616 absolute error = 8.376632720796806e-14 relative error = 3.15262949079875e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.94 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.94 Order of pole (three term test) = 3.412e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.940999999999897 y[1] (closed_form) = 0.2654293412495263 y[1] (numeric) = 0.2654293412494425 absolute error = 8.382183835919932e-14 relative error = 3.157971834033209e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.941 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.941 Order of pole (three term test) = 3.465e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.941999999999896 y[1] (closed_form) = 0.2651560549446054 y[1] (numeric) = 0.2651560549445215 absolute error = 8.382183835919932e-14 relative error = 3.161226636016697e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.942 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.942 Order of pole (three term test) = 3.519e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.942999999999896 y[1] (closed_form) = 0.2648831904862717 y[1] (numeric) = 0.2648831904861879 absolute error = 8.382183835919932e-14 relative error = 3.164483114436951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.943 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.943 Order of pole (three term test) = 7.148e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.943999999999896 y[1] (closed_form) = 0.2646107470067515 y[1] (numeric) = 0.2646107470066676 absolute error = 8.382183835919932e-14 relative error = 3.167741269293973e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.944 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.944 Order of pole (three term test) = 3.63e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.944999999999896 y[1] (closed_form) = 0.2643387236405011 y[1] (numeric) = 0.2643387236404173 absolute error = 8.387734951043058e-14 relative error = 3.173101101316627e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.945 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.945 Order of pole (three term test) = 3.686e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.945999999999896 y[1] (closed_form) = 0.2640671195242004 y[1] (numeric) = 0.2640671195241165 absolute error = 8.387734951043058e-14 relative error = 3.176364768986078e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.946 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.946 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.946999999999896 y[1] (closed_form) = 0.2637959337967455 y[1] (numeric) = 0.2637959337966616 absolute error = 8.393286066166183e-14 relative error = 3.181734435919396e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.947 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.947 Order of pole (three term test) = 7.603e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.947999999999896 y[1] (closed_form) = 0.2635251655992423 y[1] (numeric) = 0.2635251655991583 absolute error = 8.398837181289309e-14 relative error = 3.187110104718385e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.948 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.948 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.948999999999896 y[1] (closed_form) = 0.2632548140749995 y[1] (numeric) = 0.2632548140749155 absolute error = 8.398837181289309e-14 relative error = 3.190383131567934e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.949 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.949 Order of pole (three term test) = 3.92e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.949999999999896 y[1] (closed_form) = 0.2629848783695219 y[1] (numeric) = 0.2629848783694379 absolute error = 8.404388296412435e-14 relative error = 3.195768649710486e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.95 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.95 Order of pole (three term test) = 3.981e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.950999999999895 y[1] (closed_form) = 0.2627153576305037 y[1] (numeric) = 0.2627153576304197 absolute error = 8.404388296412435e-14 relative error = 3.199047201584916e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.951 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.951 Order of pole (three term test) = 8.086e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.951999999999895 y[1] (closed_form) = 0.2624462510078218 y[1] (numeric) = 0.2624462510077377 absolute error = 8.409939411535561e-14 relative error = 3.204442577952815e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.952 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.952 Order of pole (three term test) = 4.106e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.952999999999895 y[1] (closed_form) = 0.2621775576535285 y[1] (numeric) = 0.2621775576534444 absolute error = 8.409939411535561e-14 relative error = 3.20772665929302e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.953 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.953 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.953999999999895 y[1] (closed_form) = 0.2619092767218459 y[1] (numeric) = 0.2619092767217618 absolute error = 8.409939411535561e-14 relative error = 3.211012422621107e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.954 Order of pole (three term test) = 4.234e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.954999999999895 y[1] (closed_form) = 0.2616414073691583 y[1] (numeric) = 0.2616414073690742 absolute error = 8.409939411535561e-14 relative error = 3.214299867937076e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.955 Order of pole (three term test) = 8.598e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.955999999999895 y[1] (closed_form) = 0.2613739487540062 y[1] (numeric) = 0.2613739487539221 absolute error = 8.409939411535561e-14 relative error = 3.217588995240927e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.956 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.956 Order of pole (three term test) = 4.366e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.956999999999895 y[1] (closed_form) = 0.2611069000370791 y[1] (numeric) = 0.261106900036995 absolute error = 8.415490526658687e-14 relative error = 3.223005797802978e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.957 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.957 Order of pole (three term test) = 1.33e-13 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.957999999999895 y[1] (closed_form) = 0.2608402603812096 y[1] (numeric) = 0.2608402603811254 absolute error = 8.421041641781812e-14 relative error = 3.228428628876053e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.958 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.958 Order of pole (three term test) = 4.502e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.958999999999895 y[1] (closed_form) = 0.2605740289513661 y[1] (numeric) = 0.2605740289512819 absolute error = 8.421041641781812e-14 relative error = 3.231727150887139e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.959 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.959 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.959999999999894 y[1] (closed_form) = 0.2603082049146469 y[1] (numeric) = 0.2603082049145627 absolute error = 8.421041641781812e-14 relative error = 3.235027357106553e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 Order of pole (three term test) = 4.642e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.960999999999894 y[1] (closed_form) = 0.2600427874402734 y[1] (numeric) = 0.2600427874401892 absolute error = 8.426592756904938e-14 relative error = 3.240463940512234e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.961 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.961 Order of pole (three term test) = 2.357e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.961999999999894 y[1] (closed_form) = 0.2597777756995836 y[1] (numeric) = 0.2597777756994993 absolute error = 8.432143872028064e-14 relative error = 3.245906563531169e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.962 Order of pole (three term test) = 4.786e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.962999999999894 y[1] (closed_form) = 0.2595131688660255 y[1] (numeric) = 0.2595131688659412 absolute error = 8.432143872028064e-14 relative error = 3.249216180000941e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.963 Order of pole (three term test) = 7.289e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.963999999999894 y[1] (closed_form) = 0.2592489661151511 y[1] (numeric) = 0.2592489661150668 absolute error = 8.43769498715119e-14 relative error = 3.254668712315482e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.964 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.964 Order of pole (three term test) = 2.467e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.964999999999894 y[1] (closed_form) = 0.2589851666246095 y[1] (numeric) = 0.2589851666245251 absolute error = 8.43769498715119e-14 relative error = 3.257983882675933e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.965 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.965 Order of pole (three term test) = 2.505e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.965999999999894 y[1] (closed_form) = 0.2587217695741408 y[1] (numeric) = 0.2587217695740565 absolute error = 8.43769498715119e-14 relative error = 3.261300740575383e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.966 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.966 Order of pole (three term test) = 5.087e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.966999999999894 y[1] (closed_form) = 0.2584587741455697 y[1] (numeric) = 0.2584587741454852 absolute error = 8.448797217397441e-14 relative error = 3.268914837705951e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.967 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.967 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.967999999999894 y[1] (closed_form) = 0.2581961795227988 y[1] (numeric) = 0.2581961795227143 absolute error = 8.448797217397441e-14 relative error = 3.272239439410997e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.968 Order of pole (three term test) = 2.622e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.968999999999894 y[1] (closed_form) = 0.2579339848918027 y[1] (numeric) = 0.2579339848917181 absolute error = 8.454348332520567e-14 relative error = 3.277717876559372e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.969 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.969 Order of pole (three term test) = 2.663e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.969999999999893 y[1] (closed_form) = 0.2576721894406216 y[1] (numeric) = 0.257672189440537 absolute error = 8.459899447643693e-14 relative error = 3.283202376635685e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.97 Order of pole (three term test) = 8.111e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.970999999999893 y[1] (closed_form) = 0.2574107923593548 y[1] (numeric) = 0.2574107923592702 absolute error = 8.459899447643693e-14 relative error = 3.286536423008001e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.971 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.971 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.971999999999893 y[1] (closed_form) = 0.2571497928401547 y[1] (numeric) = 0.2571497928400701 absolute error = 8.459899447643693e-14 relative error = 3.289872161360207e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.972 Order of pole (three term test) = 5.574e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.972999999999893 y[1] (closed_form) = 0.2568891900772204 y[1] (numeric) = 0.2568891900771358 absolute error = 8.459899447643693e-14 relative error = 3.293209591692302e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.973 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.973 Order of pole (three term test) = 2.83e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.973999999999893 y[1] (closed_form) = 0.2566289832667916 y[1] (numeric) = 0.256628983266707 absolute error = 8.465450562766819e-14 relative error = 3.298711803711637e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.974 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.974 Order of pole (three term test) = 2.873e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.974999999999893 y[1] (closed_form) = 0.2563691716071421 y[1] (numeric) = 0.2563691716070574 absolute error = 8.465450562766819e-14 relative error = 3.302054810138874e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.975 Order of pole (three term test) = 5.834e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.975999999999893 y[1] (closed_form) = 0.2561097542985739 y[1] (numeric) = 0.2561097542984893 absolute error = 8.465450562766819e-14 relative error = 3.305399509656223e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.976 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.976 Order of pole (three term test) = 2.962e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.976999999999893 y[1] (closed_form) = 0.2558507305434112 y[1] (numeric) = 0.2558507305433266 absolute error = 8.465450562766819e-14 relative error = 3.308745902263684e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.977 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.977 Order of pole (three term test) = 3.007e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.977999999999893 y[1] (closed_form) = 0.2555920995459939 y[1] (numeric) = 0.2555920995459093 absolute error = 8.465450562766819e-14 relative error = 3.312093987961258e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.978 Order of pole (three term test) = 3.053e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.978999999999892 y[1] (closed_form) = 0.2553338605126718 y[1] (numeric) = 0.2553338605125871 absolute error = 8.471001677889944e-14 relative error = 3.317617828235336e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.979 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.979 Order of pole (three term test) = 3.1e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.979999999999892 y[1] (closed_form) = 0.255076012651798 y[1] (numeric) = 0.2550760126517133 absolute error = 8.471001677889944e-14 relative error = 3.320971497799613e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.98 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.98 Order of pole (three term test) = 3.147e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.980999999999892 y[1] (closed_form) = 0.2548185551737235 y[1] (numeric) = 0.2548185551736388 absolute error = 8.47655279301307e-14 relative error = 3.326505319533794e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.981 Order of pole (three term test) = 3.195e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.981999999999892 y[1] (closed_form) = 0.2545614872907909 y[1] (numeric) = 0.2545614872907061 absolute error = 8.482103908136196e-14 relative error = 3.332045235282158e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.982 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.982 Order of pole (three term test) = 3.244e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.982999999999892 y[1] (closed_form) = 0.2543048082173281 y[1] (numeric) = 0.2543048082172433 absolute error = 8.482103908136196e-14 relative error = 3.335408389481734e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.983 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.983 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.983999999999892 y[1] (closed_form) = 0.2540485171696427 y[1] (numeric) = 0.2540485171695578 absolute error = 8.493206138382448e-14 relative error = 3.343143362144109e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.984 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.984 Order of pole (three term test) = 6.687e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.984999999999892 y[1] (closed_form) = 0.2537926133660157 y[1] (numeric) = 0.2537926133659307 absolute error = 8.493206138382448e-14 relative error = 3.346514315660433e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.985 Order of pole (three term test) = 3.394e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.985999999999892 y[1] (closed_form) = 0.2535370960266957 y[1] (numeric) = 0.2535370960266107 absolute error = 8.498757253505573e-14 relative error = 3.352076436424401e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.986 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.986 Order of pole (three term test) = 3.446e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.986999999999892 y[1] (closed_form) = 0.2532819643738931 y[1] (numeric) = 0.2532819643738081 absolute error = 8.498757253505573e-14 relative error = 3.355452992681218e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.987 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.987 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.987999999999891 y[1] (closed_form) = 0.2530272176317739 y[1] (numeric) = 0.2530272176316888 absolute error = 8.504308368628699e-14 relative error = 3.361025129322202e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.988 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.988 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.988999999999891 y[1] (closed_form) = 0.2527728550264538 y[1] (numeric) = 0.2527728550263687 absolute error = 8.509859483751825e-14 relative error = 3.366603381071607e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.989 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.989 Order of pole (three term test) = 3.606e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.989999999999891 y[1] (closed_form) = 0.2525188757859926 y[1] (numeric) = 0.2525188757859075 absolute error = 8.509859483751825e-14 relative error = 3.369989454160192e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.99 Order of pole (three term test) = 3.661e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.990999999999891 y[1] (closed_form) = 0.2522652791403882 y[1] (numeric) = 0.2522652791403032 absolute error = 8.504308368628699e-14 relative error = 3.371176722221834e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.991 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.991 Order of pole (three term test) = 3.716e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.991999999999891 y[1] (closed_form) = 0.2520120643215708 y[1] (numeric) = 0.2520120643214857 absolute error = 8.509859483751825e-14 relative error = 3.376766706253051e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.992 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.992 Order of pole (three term test) = 3.773e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.992999999999891 y[1] (closed_form) = 0.2517592305633968 y[1] (numeric) = 0.2517592305633116 absolute error = 8.520961713998076e-14 relative error = 3.384567745512064e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.993 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.993 Order of pole (three term test) = 7.66e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.993999999999891 y[1] (closed_form) = 0.2515067771016433 y[1] (numeric) = 0.2515067771015581 absolute error = 8.520961713998076e-14 relative error = 3.387965052947434e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.994 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.994 Order of pole (three term test) = 7.776e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.994999999999891 y[1] (closed_form) = 0.2512547031740026 y[1] (numeric) = 0.2512547031739173 absolute error = 8.526512829121202e-14 relative error = 3.393573422271939e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.995 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.995999999999891 y[1] (closed_form) = 0.2510030080200756 y[1] (numeric) = 0.2510030080199904 absolute error = 8.526512829121202e-14 relative error = 3.396976353542041e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.996 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.996 Order of pole (three term test) = 4.007e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99699999999989 y[1] (closed_form) = 0.2507516908813671 y[1] (numeric) = 0.2507516908812817 absolute error = 8.532063944244328e-14 relative error = 3.402594779821814e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.997 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.997 Order of pole (three term test) = 4.067e-14 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99799999999989 y[1] (closed_form) = 0.250500751001279 y[1] (numeric) = 0.2505007510011937 absolute error = 8.532063944244328e-14 relative error = 3.406003339367539e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.998 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99899999999989 y[1] (closed_form) = 0.2502501876251056 y[1] (numeric) = 0.2502501876250203 absolute error = 8.532063944244328e-14 relative error = 3.409413605326054e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 1.999 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.999 Order of pole (three term test) = 0 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.99999999999989 y[1] (closed_form) = 0.2500000000000275 y[1] (numeric) = 0.2499999999999421 absolute error = 8.54316617449058e-14 relative error = 3.417266469795856e-11 % Desired digits = 8 Estimated correct digits = 11 Correct digits = 13 h = -0.001 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 2 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2 Order of pole (three term test) = 4.255e-14 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = neg ( 2.0 ) / x / x / x ; Iterations = 1301 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Expected Time Remaining = 0.0 Seconds Optimized Time Remaining = 0.0 Seconds Expected Total Time = 0.0 Seconds Time to Timeout = 3 Minutes 0.0 Seconds Percent Done = 0 %