##############ECHO OF PROBLEM################# ##############temp/arctan_sqrtpostode.ode################# diff ( y , x , 1 ) = arctan(sqrt(0.1 * x + 0.2)); ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-1.0; x_end=0.5; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_max_iter=1000000; glob_display_interval=0.1; glob_max_minutes=10; // END SECOND INPUT BLOCK // BEGIN OVERRIDE BLOCK glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=10000000; glob_max_minutes=3; glob_subiter_method=3; // END OVERRIDE BLOCK ! // BEGIN USER DEF BLOCK double exact_soln_y (double x) { return(10.0 * (0.1 * x + 0.2) * arctan(sqrt ( 0.1 * x + 0.2)) - 10.0 * sqrt( 0.1 * x + 0.2) + 10.0 * arctan(sqrt( 0.1 * x + 0.2))); } // END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1e-10 range = 1.5 estimated_steps = 1500000 step_error = 6.666666666666667e-17 est_needed_step_err = 6.666666666666667e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.792822763189861e-161 estimated_step_error = 2.792822763189861e-161 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.874230779639759e-153 estimated_step_error = 1.874230779639759e-153 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.257773843742575e-145 estimated_step_error = 1.257773843742575e-145 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.440762065201303e-138 estimated_step_error = 8.440762065201303e-138 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.664478976820091e-130 estimated_step_error = 5.664478976820091e-130 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.801339900577164e-122 estimated_step_error = 3.801339900577164e-122 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.550998991126603e-114 estimated_step_error = 2.550998991126603e-114 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.711896741012717e-106 estimated_step_error = 1.711896741012717e-106 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.148767751900283e-98 estimated_step_error = 1.148767751900283e-98 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.708354755676755e-91 estimated_step_error = 7.708354755676755e-91 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.171788310353771e-83 estimated_step_error = 5.171788310353771e-83 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.469117557772959e-75 estimated_step_error = 3.469117557772959e-75 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.325926398407867e-67 estimated_step_error = 2.325926398407867e-67 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.558013171381974e-59 estimated_step_error = 1.558013171381974e-59 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.041708390108846e-51 estimated_step_error = 1.041708390108846e-51 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.939610693763538e-44 estimated_step_error = 6.939610693763538e-44 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.589979076596559e-36 estimated_step_error = 4.589979076596559e-36 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.994423710885246e-28 estimated_step_error = 2.994423710885246e-28 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -1 y[1] (analytic) = 0.2067734006979847 y[1] (numeric) = 0.2067734006979847 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.122 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.008 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.99 y[1] (analytic) = 0.209843347279264 y[1] (numeric) = 0.2098433472792642 absolute error = 2.220446049250313e-16 relative error = 1.058144600741284e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.133 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.029 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.98 y[1] (analytic) = 0.2129275836241563 y[1] (numeric) = 0.2129275836241566 absolute error = 2.498001805406602e-16 relative error = 1.173169658382958e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.145 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.05 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.97 y[1] (analytic) = 0.2160260266070556 y[1] (numeric) = 0.2160260266070556 absolute error = 8.326672684688674e-17 relative error = 3.854476618150563e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.156 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.071 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.96 y[1] (analytic) = 0.2191385942764166 y[1] (numeric) = 0.2191385942764168 absolute error = 1.942890293094024e-16 relative error = 8.866034299021306e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.167 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.092 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.95 y[1] (analytic) = 0.2222652058269296 y[1] (numeric) = 0.2222652058269294 absolute error = 1.942890293094024e-16 relative error = 8.741315519294042e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.178 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.113 Order of pole (six term test) = -0.5994 TOP MAIN SOLVE Loop x[1] = -0.9399999999999999 y[1] (analytic) = 0.2254057815726103 y[1] (numeric) = 0.2254057815726104 absolute error = 1.387778780781446e-16 relative error = 6.156802062037608e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.189 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.133 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.9299999999999999 y[1] (analytic) = 0.2285602429207843 y[1] (numeric) = 0.2285602429207844 absolute error = 2.775557561562891e-17 relative error = 1.214365860874964e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.201 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.154 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.9199999999999999 y[1] (analytic) = 0.2317285123469087 y[1] (numeric) = 0.2317285123469088 absolute error = 5.551115123125783e-17 relative error = 2.395525292466167e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.212 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.174 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.9099999999999999 y[1] (analytic) = 0.2349105133702123 y[1] (numeric) = 0.2349105133702122 absolute error = 5.551115123125783e-17 relative error = 2.363076493889136e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.223 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.195 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.8999999999999999 y[1] (analytic) = 0.2381061705301104 y[1] (numeric) = 0.2381061705301102 absolute error = 2.775557561562891e-16 relative error = 1.165680652199603e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.234 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.215 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.8899999999999999 y[1] (analytic) = 0.2413154093633677 y[1] (numeric) = 0.2413154093633676 absolute error = 1.387778780781446e-16 relative error = 5.750891683389175e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.246 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.235 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.8799999999999999 y[1] (analytic) = 0.2445381563819782 y[1] (numeric) = 0.2445381563819778 absolute error = 3.885780586188048e-16 relative error = 1.589028331479814e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.257 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.255 Order of pole (six term test) = -0.5995 TOP MAIN SOLVE Loop x[1] = -0.8699999999999999 y[1] (analytic) = 0.2477743390517293 y[1] (numeric) = 0.2477743390517292 absolute error = 1.665334536937735e-16 relative error = 6.721174369029607e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.268 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.276 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8599999999999999 y[1] (analytic) = 0.2510238857714306 y[1] (numeric) = 0.2510238857714311 absolute error = 4.440892098500626e-16 relative error = 1.769111367570922e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.279 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.296 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8499999999999999 y[1] (analytic) = 0.2542867258527755 y[1] (numeric) = 0.2542867258527754 absolute error = 5.551115123125783e-17 relative error = 2.18301411704035e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.315 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8399999999999999 y[1] (analytic) = 0.2575627895008061 y[1] (numeric) = 0.2575627895008064 absolute error = 2.220446049250313e-16 relative error = 8.620989287908622e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.302 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.335 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8299999999999998 y[1] (analytic) = 0.2608520077949769 y[1] (numeric) = 0.2608520077949769 absolute error = 5.551115123125783e-17 relative error = 2.128070690369698e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.313 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.355 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8199999999999998 y[1] (analytic) = 0.2641543126707679 y[1] (numeric) = 0.2641543126707679 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.324 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.375 Order of pole (six term test) = -0.5996 TOP MAIN SOLVE Loop x[1] = -0.8099999999999998 y[1] (analytic) = 0.26746963690185 y[1] (numeric) = 0.2674696369018499 absolute error = 1.665334536937735e-16 relative error = 6.226256393913009e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.335 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.394 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7999999999999998 y[1] (analytic) = 0.2707979140827654 y[1] (numeric) = 0.2707979140827652 absolute error = 1.665334536937735e-16 relative error = 6.149731775366446e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.347 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.414 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7899999999999998 y[1] (analytic) = 0.2741390786121137 y[1] (numeric) = 0.2741390786121136 absolute error = 1.665334536937735e-16 relative error = 6.074779799249484e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.358 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.434 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7799999999999998 y[1] (analytic) = 0.277493065676219 y[1] (numeric) = 0.2774930656762195 absolute error = 4.996003610813204e-16 relative error = 1.80040665111343e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.369 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.453 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7699999999999998 y[1] (analytic) = 0.2808598112332662 y[1] (numeric) = 0.2808598112332664 absolute error = 1.665334536937735e-16 relative error = 5.929415567236861e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.472 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7599999999999998 y[1] (analytic) = 0.2842392519978783 y[1] (numeric) = 0.2842392519978782 absolute error = 5.551115123125783e-17 relative error = 1.952972745357218e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.391 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.492 Order of pole (six term test) = -0.5997 TOP MAIN SOLVE Loop x[1] = -0.7499999999999998 y[1] (analytic) = 0.2876313254261343 y[1] (numeric) = 0.2876313254261343 absolute error = 5.551115123125783e-17 relative error = 1.929941085137942e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.403 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.511 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.7399999999999998 y[1] (analytic) = 0.2910359697010003 y[1] (numeric) = 0.2910359697010005 absolute error = 1.665334536937735e-16 relative error = 5.722091804145853e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.414 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.53 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.7299999999999998 y[1] (analytic) = 0.2944531237181621 y[1] (numeric) = 0.2944531237181622 absolute error = 1.110223024625157e-16 relative error = 3.770457621933108e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.425 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.549 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.7199999999999998 y[1] (analytic) = 0.2978827270722454 y[1] (numeric) = 0.2978827270722452 absolute error = 2.775557561562891e-16 relative error = 9.317618342099224e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.436 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.568 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.7099999999999997 y[1] (analytic) = 0.3013247200434107 y[1] (numeric) = 0.3013247200434108 absolute error = 1.665334536937735e-16 relative error = 5.526710641920838e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.448 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.587 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.6999999999999997 y[1] (analytic) = 0.3047790435843115 y[1] (numeric) = 0.304779043584312 absolute error = 4.440892098500626e-16 relative error = 1.45708577803583e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.459 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.606 Order of pole (six term test) = -0.5998 TOP MAIN SOLVE Loop x[1] = -0.6899999999999997 y[1] (analytic) = 0.3082456393073974 y[1] (numeric) = 0.3082456393073977 absolute error = 2.775557561562891e-16 relative error = 9.004369267962204e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.625 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6799999999999997 y[1] (analytic) = 0.3117244494725546 y[1] (numeric) = 0.3117244494725548 absolute error = 2.220446049250313e-16 relative error = 7.123105207202586e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.481 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.644 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6699999999999997 y[1] (analytic) = 0.3152154169750747 y[1] (numeric) = 0.3152154169750747 absolute error = 5.551115123125783e-17 relative error = 1.761054448540736e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.492 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.663 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6599999999999997 y[1] (analytic) = 0.3187184853339337 y[1] (numeric) = 0.3187184853339339 absolute error = 2.775557561562891e-16 relative error = 8.708492570347254e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.504 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.681 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6499999999999997 y[1] (analytic) = 0.3222335986803793 y[1] (numeric) = 0.3222335986803793 absolute error = 5.551115123125783e-17 relative error = 1.722699043755485e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.515 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.7 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6399999999999997 y[1] (analytic) = 0.325760701746806 y[1] (numeric) = 0.325760701746806 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.526 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.719 Order of pole (six term test) = -0.5999 TOP MAIN SOLVE Loop x[1] = -0.6299999999999997 y[1] (analytic) = 0.3292997398559201 y[1] (numeric) = 0.3292997398559204 absolute error = 2.775557561562891e-16 relative error = 8.428666122777056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.537 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.737 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.6199999999999997 y[1] (analytic) = 0.3328506589101768 y[1] (numeric) = 0.3328506589101765 absolute error = 3.885780586188048e-16 relative error = 1.167424633891641e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.549 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.756 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.6099999999999997 y[1] (analytic) = 0.336413405381479 y[1] (numeric) = 0.3364134053814792 absolute error = 2.220446049250313e-16 relative error = 6.600349491817718e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.774 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.5999999999999996 y[1] (analytic) = 0.3399879263011442 y[1] (numeric) = 0.3399879263011443 absolute error = 1.110223024625157e-16 relative error = 3.265477797119704e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.571 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.792 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.5899999999999996 y[1] (analytic) = 0.3435741692501068 y[1] (numeric) = 0.343574169250107 absolute error = 2.220446049250313e-16 relative error = 6.462785179970635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.582 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.811 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.5799999999999996 y[1] (analytic) = 0.3471720823493723 y[1] (numeric) = 0.3471720823493722 absolute error = 5.551115123125783e-17 relative error = 1.598952048667176e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.593 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.829 Order of pole (six term test) = -0.6 TOP MAIN SOLVE Loop x[1] = -0.5699999999999996 y[1] (analytic) = 0.3507816142506976 y[1] (numeric) = 0.3507816142506978 absolute error = 1.665334536937735e-16 relative error = 4.747496645441481e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.605 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.847 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5599999999999996 y[1] (analytic) = 0.3544027141275038 y[1] (numeric) = 0.354402714127504 absolute error = 1.665334536937735e-16 relative error = 4.698989230479188e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.616 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.865 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5499999999999996 y[1] (analytic) = 0.3580353316660019 y[1] (numeric) = 0.3580353316660019 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.627 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.884 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5399999999999996 y[1] (analytic) = 0.3616794170565339 y[1] (numeric) = 0.3616794170565342 absolute error = 2.775557561562891e-16 relative error = 7.674082158590312e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.638 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.902 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5299999999999996 y[1] (analytic) = 0.3653349209851213 y[1] (numeric) = 0.3653349209851217 absolute error = 3.33066907387547e-16 relative error = 9.116755290992604e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.92 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5199999999999996 y[1] (analytic) = 0.3690017946252092 y[1] (numeric) = 0.3690017946252093 absolute error = 1.110223024625157e-16 relative error = 3.008719851221312e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.661 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.938 Order of pole (six term test) = -0.6001 TOP MAIN SOLVE Loop x[1] = -0.5099999999999996 y[1] (analytic) = 0.3726799896296057 y[1] (numeric) = 0.3726799896296057 absolute error = 5.551115123125783e-17 relative error = 1.489512524845472e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.672 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.955 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4999999999999996 y[1] (analytic) = 0.37636945812261 y[1] (numeric) = 0.3763694581226099 absolute error = 1.665334536937735e-16 relative error = 4.424733466006208e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.683 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.973 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4899999999999995 y[1] (analytic) = 0.3800701526923206 y[1] (numeric) = 0.3800701526923205 absolute error = 1.110223024625157e-16 relative error = 2.921100267307543e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.991 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4799999999999995 y[1] (analytic) = 0.3837820263831215 y[1] (numeric) = 0.3837820263831218 absolute error = 2.775557561562891e-16 relative error = 7.232119720979613e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.706 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.009 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4699999999999995 y[1] (analytic) = 0.3875050326883402 y[1] (numeric) = 0.3875050326883402 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.717 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.027 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4599999999999995 y[1] (analytic) = 0.3912391255430681 y[1] (numeric) = 0.3912391255430681 absolute error = 5.551115123125783e-17 relative error = 1.418854802780892e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.728 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.044 Order of pole (six term test) = -0.6002 TOP MAIN SOLVE Loop x[1] = -0.4499999999999995 y[1] (analytic) = 0.3949842593171487 y[1] (numeric) = 0.3949842593171487 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.739 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.062 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.4399999999999995 y[1] (analytic) = 0.3987403888083179 y[1] (numeric) = 0.3987403888083179 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.751 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.08 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.4299999999999995 y[1] (analytic) = 0.4025074692354986 y[1] (numeric) = 0.4025074692354986 absolute error = 5.551115123125783e-17 relative error = 1.379133444074784e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.762 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.097 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.4199999999999995 y[1] (analytic) = 0.4062854562322431 y[1] (numeric) = 0.4062854562322429 absolute error = 1.665334536937735e-16 relative error = 4.098927272419486e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.773 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.115 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.4099999999999995 y[1] (analytic) = 0.410074305840318 y[1] (numeric) = 0.4100743058403182 absolute error = 2.775557561562891e-16 relative error = 6.768425921919837e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.784 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.132 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.3999999999999995 y[1] (analytic) = 0.4138739745034328 y[1] (numeric) = 0.4138739745034329 absolute error = 5.551115123125783e-17 relative error = 1.341257354919701e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.795 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.15 Order of pole (six term test) = -0.6003 TOP MAIN SOLVE Loop x[1] = -0.3899999999999995 y[1] (analytic) = 0.4176844190610982 y[1] (numeric) = 0.4176844190610981 absolute error = 5.551115123125783e-17 relative error = 1.329021354352645e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.807 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.167 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3799999999999994 y[1] (analytic) = 0.4215055967426212 y[1] (numeric) = 0.4215055967426217 absolute error = 4.996003610813204e-16 relative error = 1.185275747089037e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.818 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.184 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3699999999999994 y[1] (analytic) = 0.4253374651612302 y[1] (numeric) = 0.4253374651612299 absolute error = 2.220446049250313e-16 relative error = 5.220433728800781e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.829 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.202 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3599999999999994 y[1] (analytic) = 0.4291799823083154 y[1] (numeric) = 0.4291799823083152 absolute error = 1.665334536937735e-16 relative error = 3.880270761886065e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.219 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3499999999999994 y[1] (analytic) = 0.433033106547804 y[1] (numeric) = 0.433033106547804 absolute error = 5.551115123125783e-17 relative error = 1.281914717186404e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.852 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.236 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3399999999999994 y[1] (analytic) = 0.4368967966106439 y[1] (numeric) = 0.4368967966106438 absolute error = 5.551115123125783e-17 relative error = 1.270578124213819e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.863 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.253 Order of pole (six term test) = -0.6004 TOP MAIN SOLVE Loop x[1] = -0.3299999999999994 y[1] (analytic) = 0.440771011589405 y[1] (numeric) = 0.4407710115894052 absolute error = 2.220446049250313e-16 relative error = 5.037640840407045e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.874 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.27 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.3199999999999994 y[1] (analytic) = 0.4446557109329952 y[1] (numeric) = 0.4446557109329948 absolute error = 3.33066907387547e-16 relative error = 7.490444836268763e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.885 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.287 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.3099999999999994 y[1] (analytic) = 0.4485508544414787 y[1] (numeric) = 0.4485508544414787 absolute error = 5.551115123125783e-17 relative error = 1.237566502919241e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.897 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.304 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.2999999999999994 y[1] (analytic) = 0.4524564022610102 y[1] (numeric) = 0.4524564022610101 absolute error = 5.551115123125783e-17 relative error = 1.226883981613656e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.908 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.322 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.2899999999999994 y[1] (analytic) = 0.4563723148788621 y[1] (numeric) = 0.4563723148788622 absolute error = 1.110223024625157e-16 relative error = 2.432713353613158e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.919 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.338 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.2799999999999994 y[1] (analytic) = 0.4602985531185599 y[1] (numeric) = 0.4602985531185598 absolute error = 1.665334536937735e-16 relative error = 3.617944322559692e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.355 Order of pole (six term test) = -0.6005 TOP MAIN SOLVE Loop x[1] = -0.2699999999999994 y[1] (analytic) = 0.4642350781351101 y[1] (numeric) = 0.46423507813511 absolute error = 5.551115123125783e-17 relative error = 1.195755207776479e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.941 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.372 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2599999999999993 y[1] (analytic) = 0.4681818514103283 y[1] (numeric) = 0.468181851410328 absolute error = 2.775557561562891e-16 relative error = 5.928374953454381e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.953 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.389 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2499999999999993 y[1] (analytic) = 0.4721388347482555 y[1] (numeric) = 0.4721388347482557 absolute error = 1.665334536937735e-16 relative error = 3.527213637966662e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.964 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.406 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2399999999999993 y[1] (analytic) = 0.476105990270671 y[1] (numeric) = 0.4761059902706709 absolute error = 1.110223024625157e-16 relative error = 2.331882075237036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.975 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.423 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2299999999999993 y[1] (analytic) = 0.4800832804126849 y[1] (numeric) = 0.4800832804126848 absolute error = 1.665334536937735e-16 relative error = 3.468845104345635e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.986 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.44 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2199999999999993 y[1] (analytic) = 0.4840706679184257 y[1] (numeric) = 0.4840706679184257 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 1.998 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.456 Order of pole (six term test) = -0.6006 TOP MAIN SOLVE Loop x[1] = -0.2099999999999993 y[1] (analytic) = 0.4880681158368063 y[1] (numeric) = 0.4880681158368065 absolute error = 2.220446049250313e-16 relative error = 4.549459342254507e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.009 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.473 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1999999999999993 y[1] (analytic) = 0.4920755875173736 y[1] (numeric) = 0.4920755875173733 absolute error = 2.220446049250313e-16 relative error = 4.512408470521648e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.49 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1899999999999993 y[1] (analytic) = 0.4960930466062353 y[1] (numeric) = 0.4960930466062352 absolute error = 1.110223024625157e-16 relative error = 2.237933049495805e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.031 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.506 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1799999999999993 y[1] (analytic) = 0.5001204570420702 y[1] (numeric) = 0.5001204570420702 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.042 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.523 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1699999999999993 y[1] (analytic) = 0.5041577830522078 y[1] (numeric) = 0.5041577830522082 absolute error = 3.33066907387547e-16 relative error = 6.606402173762661e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.054 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.539 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1599999999999993 y[1] (analytic) = 0.5082049891487874 y[1] (numeric) = 0.5082049891487873 absolute error = 1.110223024625157e-16 relative error = 2.184596862153425e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.065 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.556 Order of pole (six term test) = -0.6007 TOP MAIN SOLVE Loop x[1] = -0.1499999999999992 y[1] (analytic) = 0.5122620401249831 y[1] (numeric) = 0.512262040124983 absolute error = 1.110223024625157e-16 relative error = 2.16729512956744e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.076 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.572 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.1399999999999992 y[1] (analytic) = 0.5163289010513065 y[1] (numeric) = 0.5163289010513068 absolute error = 3.33066907387547e-16 relative error = 6.450673334562205e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.087 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.589 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.1299999999999992 y[1] (analytic) = 0.5204055372719747 y[1] (numeric) = 0.5204055372719745 absolute error = 2.220446049250313e-16 relative error = 4.266760997375518e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.099 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.605 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.1199999999999992 y[1] (analytic) = 0.5244919144013416 y[1] (numeric) = 0.5244919144013414 absolute error = 2.220446049250313e-16 relative error = 4.233518169264333e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.621 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.1099999999999992 y[1] (analytic) = 0.5285879983204026 y[1] (numeric) = 0.5285879983204025 absolute error = 1.110223024625157e-16 relative error = 2.100356096152219e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.121 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.638 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.09999999999999924 y[1] (analytic) = 0.5326937551733574 y[1] (numeric) = 0.5326937551733575 absolute error = 1.110223024625157e-16 relative error = 2.084167523728246e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.132 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.654 Order of pole (six term test) = -0.6008 TOP MAIN SOLVE Loop x[1] = -0.08999999999999925 y[1] (analytic) = 0.5368091513642375 y[1] (numeric) = 0.5368091513642377 absolute error = 2.220446049250313e-16 relative error = 4.136378904136247e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.143 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.67 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.07999999999999925 y[1] (analytic) = 0.5409341535535939 y[1] (numeric) = 0.5409341535535939 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.155 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.687 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.06999999999999926 y[1] (analytic) = 0.5450687286552441 y[1] (numeric) = 0.5450687286552441 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.166 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.703 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.05999999999999926 y[1] (analytic) = 0.5492128438330797 y[1] (numeric) = 0.5492128438330796 absolute error = 1.110223024625157e-16 relative error = 2.02148044622675e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.177 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.719 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.04999999999999925 y[1] (analytic) = 0.5533664664979269 y[1] (numeric) = 0.5533664664979271 absolute error = 2.220446049250313e-16 relative error = 4.012614033703164e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.188 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.735 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.03999999999999925 y[1] (analytic) = 0.5575295643044673 y[1] (numeric) = 0.5575295643044675 absolute error = 2.220446049250313e-16 relative error = 3.982651668024775e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.751 Order of pole (six term test) = -0.6009 TOP MAIN SOLVE Loop x[1] = -0.02999999999999925 y[1] (analytic) = 0.5617021051482078 y[1] (numeric) = 0.5617021051482083 absolute error = 4.440892098500626e-16 relative error = 7.906133977064008e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.211 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.767 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = -0.01999999999999925 y[1] (analytic) = 0.5658840571625083 y[1] (numeric) = 0.5658840571625088 absolute error = 4.440892098500626e-16 relative error = 7.847706685303043e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.222 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.783 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = -0.009999999999999247 y[1] (analytic) = 0.5700753887156579 y[1] (numeric) = 0.570075388715658 absolute error = 1.110223024625157e-16 relative error = 1.947502113933414e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.233 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.799 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = 7.528699885739343e-16 y[1] (analytic) = 0.5742760684080025 y[1] (numeric) = 0.5742760684080027 absolute error = 2.220446049250313e-16 relative error = 3.866513287600148e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.244 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.815 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = 0.01000000000000075 y[1] (analytic) = 0.5784860650691246 y[1] (numeric) = 0.5784860650691249 absolute error = 3.33066907387547e-16 relative error = 5.757561460840859e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.256 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.831 Order of pole (six term test) = -0.601 TOP MAIN SOLVE Loop x[1] = 0.02000000000000075 y[1] (analytic) = 0.5827053477550682 y[1] (numeric) = 0.5827053477550682 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.267 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.847 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.03000000000000076 y[1] (analytic) = 0.5869338857456107 y[1] (numeric) = 0.5869338857456113 absolute error = 6.661338147750939e-16 relative error = 1.134938416324135e-13 % Correct digits = 15 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.278 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.863 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.04000000000000076 y[1] (analytic) = 0.5911716485415879 y[1] (numeric) = 0.591171648541588 absolute error = 1.110223024625157e-16 relative error = 1.878004514194923e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.289 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.879 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.05000000000000076 y[1] (analytic) = 0.5954186058622515 y[1] (numeric) = 0.595418605862252 absolute error = 5.551115123125783e-16 relative error = 9.323046119942745e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.301 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.895 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.06000000000000076 y[1] (analytic) = 0.5996747276426873 y[1] (numeric) = 0.599674727642687 absolute error = 2.220446049250313e-16 relative error = 3.702750752860396e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.312 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.911 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.07000000000000076 y[1] (analytic) = 0.603939984031259 y[1] (numeric) = 0.6039399840312594 absolute error = 3.33066907387547e-16 relative error = 5.514900754945013e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.323 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.927 Order of pole (six term test) = -0.6011 TOP MAIN SOLVE Loop x[1] = 0.08000000000000075 y[1] (analytic) = 0.6082143453871136 y[1] (numeric) = 0.6082143453871135 absolute error = 1.110223024625157e-16 relative error = 1.825381188466587e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.334 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.942 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.09000000000000075 y[1] (analytic) = 0.612497782277709 y[1] (numeric) = 0.6124977822777088 absolute error = 2.220446049250313e-16 relative error = 3.625231165724537e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.346 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.958 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.1000000000000007 y[1] (analytic) = 0.6167902654763973 y[1] (numeric) = 0.6167902654763971 absolute error = 1.110223024625157e-16 relative error = 1.800000886472553e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.357 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.974 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.1100000000000007 y[1] (analytic) = 0.6210917659600405 y[1] (numeric) = 0.6210917659600406 absolute error = 1.110223024625157e-16 relative error = 1.787534605146554e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.368 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.99 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.1200000000000007 y[1] (analytic) = 0.625402254906667 y[1] (numeric) = 0.625402254906667 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.379 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.005 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.1300000000000007 y[1] (analytic) = 0.6297217036931647 y[1] (numeric) = 0.629721703693165 absolute error = 3.33066907387547e-16 relative error = 5.28911272128927e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.021 Order of pole (six term test) = -0.6012 TOP MAIN SOLVE Loop x[1] = 0.1400000000000007 y[1] (analytic) = 0.6340500838930151 y[1] (numeric) = 0.6340500838930155 absolute error = 4.440892098500626e-16 relative error = 7.004008376174191e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.402 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.036 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.1500000000000007 y[1] (analytic) = 0.63838736727406 y[1] (numeric) = 0.6383873672740599 absolute error = 1.110223024625157e-16 relative error = 1.739105567464241e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.413 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.052 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.1600000000000008 y[1] (analytic) = 0.6427335257963039 y[1] (numeric) = 0.6427335257963041 absolute error = 1.110223024625157e-16 relative error = 1.727345750713197e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.424 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.068 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.1700000000000008 y[1] (analytic) = 0.6470885316097572 y[1] (numeric) = 0.6470885316097575 absolute error = 3.33066907387547e-16 relative error = 5.147161340643435e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.435 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.083 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.1800000000000008 y[1] (analytic) = 0.6514523570523068 y[1] (numeric) = 0.651452357052307 absolute error = 2.220446049250313e-16 relative error = 3.408455008586342e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.447 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.099 Order of pole (six term test) = -0.6013 TOP MAIN SOLVE Loop x[1] = 0.1900000000000008 y[1] (analytic) = 0.6558249746476226 y[1] (numeric) = 0.6558249746476228 absolute error = 2.220446049250313e-16 relative error = 3.385729630749984e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.458 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.114 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2000000000000008 y[1] (analytic) = 0.6602063571030989 y[1] (numeric) = 0.6602063571030995 absolute error = 5.551115123125783e-16 relative error = 8.408151577763301e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.469 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.129 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2100000000000008 y[1] (analytic) = 0.6645964773078271 y[1] (numeric) = 0.6645964773078277 absolute error = 5.551115123125783e-16 relative error = 8.35260991092287e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.145 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2200000000000008 y[1] (analytic) = 0.6689953083305981 y[1] (numeric) = 0.6689953083305979 absolute error = 1.110223024625157e-16 relative error = 1.659537833524711e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.491 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.16 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2300000000000008 y[1] (analytic) = 0.6734028234179353 y[1] (numeric) = 0.6734028234179357 absolute error = 3.33066907387547e-16 relative error = 4.946027783148081e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.503 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.176 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2400000000000008 y[1] (analytic) = 0.6778189959921654 y[1] (numeric) = 0.6778189959921659 absolute error = 4.440892098500626e-16 relative error = 6.551737447252003e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.514 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.191 Order of pole (six term test) = -0.6014 TOP MAIN SOLVE Loop x[1] = 0.2500000000000008 y[1] (analytic) = 0.6822437996495085 y[1] (numeric) = 0.6822437996495085 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.525 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.206 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.2600000000000008 y[1] (analytic) = 0.6866772081582023 y[1] (numeric) = 0.6866772081582023 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.536 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.222 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.2700000000000009 y[1] (analytic) = 0.6911191954566572 y[1] (numeric) = 0.6911191954566575 absolute error = 2.220446049250313e-16 relative error = 3.212826476022204e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.548 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.237 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.2800000000000009 y[1] (analytic) = 0.695569735651636 y[1] (numeric) = 0.6955697356516362 absolute error = 1.110223024625157e-16 relative error = 1.59613474784819e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.559 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.252 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.2900000000000009 y[1] (analytic) = 0.7000288030164611 y[1] (numeric) = 0.700028803016461 absolute error = 1.110223024625157e-16 relative error = 1.585967634247544e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.267 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.3000000000000009 y[1] (analytic) = 0.70449637198925 y[1] (numeric) = 0.7044963719892496 absolute error = 3.33066907387547e-16 relative error = 4.727730626164662e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.581 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.283 Order of pole (six term test) = -0.6015 TOP MAIN SOLVE Loop x[1] = 0.3100000000000009 y[1] (analytic) = 0.7089724171711763 y[1] (numeric) = 0.7089724171711768 absolute error = 4.440892098500626e-16 relative error = 6.263843262365459e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.592 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.298 Order of pole (six term test) = -0.6016 TOP MAIN SOLVE Loop x[1] = 0.3200000000000009 y[1] (analytic) = 0.7134569133247609 y[1] (numeric) = 0.7134569133247611 absolute error = 2.220446049250313e-16 relative error = 3.112235662421258e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.604 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.313 Order of pole (six term test) = -0.6016 TOP MAIN SOLVE Loop x[1] = 0.3300000000000009 y[1] (analytic) = 0.717949835372178 y[1] (numeric) = 0.7179498353721784 absolute error = 3.33066907387547e-16 relative error = 4.639138989632728e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.615 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.328 Order of pole (six term test) = -0.6016 TOP MAIN SOLVE Loop x[1] = 0.3400000000000009 y[1] (analytic) = 0.7224511583935993 y[1] (numeric) = 0.722451158393599 absolute error = 3.33066907387547e-16 relative error = 4.61023424930393e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.626 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.343 Order of pole (six term test) = -0.6016 TOP MAIN SOLVE Loop x[1] = 0.3500000000000009 y[1] (analytic) = 0.7269608576255501 y[1] (numeric) = 0.7269608576255503 absolute error = 2.220446049250313e-16 relative error = 3.054423117776778e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.637 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.358 Order of pole (six term test) = -0.6016 TOP MAIN SOLVE Loop x[1] = 0.3600000000000009 y[1] (analytic) = 0.7314789084593024 y[1] (numeric) = 0.7314789084593026 absolute error = 2.220446049250313e-16 relative error = 3.035557175431331e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.649 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.373 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.3700000000000009 y[1] (analytic) = 0.7360052864392791 y[1] (numeric) = 0.736005286439279 absolute error = 1.110223024625157e-16 relative error = 1.508444361855478e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.388 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.3800000000000009 y[1] (analytic) = 0.7405399672614874 y[1] (numeric) = 0.7405399672614879 absolute error = 4.440892098500626e-16 relative error = 5.996829738876916e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.671 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.403 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.390000000000001 y[1] (analytic) = 0.7450829267719782 y[1] (numeric) = 0.7450829267719786 absolute error = 4.440892098500626e-16 relative error = 5.960265547541793e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.682 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.418 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.400000000000001 y[1] (analytic) = 0.7496341409653191 y[1] (numeric) = 0.7496341409653192 absolute error = 1.110223024625157e-16 relative error = 1.481019825478466e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.694 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.433 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.410000000000001 y[1] (analytic) = 0.7541935859830955 y[1] (numeric) = 0.7541935859830955 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.705 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.448 Order of pole (six term test) = -0.6017 TOP MAIN SOLVE Loop x[1] = 0.420000000000001 y[1] (analytic) = 0.7587612381124321 y[1] (numeric) = 0.7587612381124323 absolute error = 2.220446049250313e-16 relative error = 2.926409439119623e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.716 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.463 Order of pole (six term test) = -0.6018 TOP MAIN SOLVE Loop x[1] = 0.430000000000001 y[1] (analytic) = 0.7633370737845354 y[1] (numeric) = 0.7633370737845354 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.727 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.478 Order of pole (six term test) = -0.6018 TOP MAIN SOLVE Loop x[1] = 0.440000000000001 y[1] (analytic) = 0.7679210695732538 y[1] (numeric) = 0.7679210695732536 absolute error = 2.220446049250313e-16 relative error = 2.891502964600582e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.738 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.493 Order of pole (six term test) = -0.6018 TOP MAIN SOLVE Loop x[1] = 0.450000000000001 y[1] (analytic) = 0.7725132021936623 y[1] (numeric) = 0.7725132021936618 absolute error = 4.440892098500626e-16 relative error = 5.748629390268121e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.508 Order of pole (six term test) = -0.6018 TOP MAIN SOLVE Loop x[1] = 0.460000000000001 y[1] (analytic) = 0.7771134485006643 y[1] (numeric) = 0.7771134485006641 absolute error = 2.220446049250313e-16 relative error = 2.857299733435786e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.761 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.523 Order of pole (six term test) = -0.6018 TOP MAIN SOLVE Loop x[1] = 0.470000000000001 y[1] (analytic) = 0.7817217854876154 y[1] (numeric) = 0.7817217854876153 absolute error = 1.110223024625157e-16 relative error = 1.420227816642761e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.772 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.537 Order of pole (six term test) = -0.6019 TOP MAIN SOLVE Loop x[1] = 0.480000000000001 y[1] (analytic) = 0.7863381902849629 y[1] (numeric) = 0.7863381902849627 absolute error = 2.220446049250313e-16 relative error = 2.823779992735239e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.783 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.552 Order of pole (six term test) = -0.6019 TOP MAIN SOLVE Loop x[1] = 0.490000000000001 y[1] (analytic) = 0.7909626401589063 y[1] (numeric) = 0.790962640158906 absolute error = 2.220446049250313e-16 relative error = 2.807270453133185e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 2.795 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.567 Order of pole (six term test) = -0.6019 Finished! diff ( y , x , 1 ) = arctan(sqrt(0.1 * x + 0.2)); Iterations = 150 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 100.7 %