##############ECHO OF PROBLEM################# ##############temp/sing6postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ; ! #BEGIN FIRST INPUT BLOCK # Digits:=64; ELIMINATED in preodein.rb max_terms=40 ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start=2.0 x_end=3.0 $array_y_init[0 + 1] = exact_soln_y(x_start) $glob_look_poles=true $glob_max_iter=100 ## Not Given = 0 ## No Pole = 3 ## Pole = 4 $glob_type_given_pole=4 ## Real Part $array_given_rad_poles[1][1]=6.0 ## Imag Part $array_given_rad_poles[1][2]=0.0 ## Order $array_given_ord_poles[1][1]=3.0 ## Not Used $array_given_ord_poles[1][2]=0.0 #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 def exact_soln_y (x) return(1.0/ ( x - 6.0 ) / ( x - 6.0 )) end #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size 0.0 min_size 1.0 $glob_desired_digits_correct 10 desired_abs_gbl_error 1.0e-10 range 1.0 estimated_steps 1000000.0 step_error 1.0e-16 est_needed_step_err 1.0e-16 opt_iter 1 hn_div_ho 0.5 hn_div_ho_2 0.25 hn_div_ho_3 0.125 max_estimated_step_error 1.1029076175414484e-239 estimated_step_error 1.1029076175414484e-239 best_h 2.0e-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 7.57912435834518e-229 estimated_step_error 7.57912435834518e-229 best_h 4.0e-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 5.208335867118343e-218 estimated_step_error 5.208335867118343e-218 best_h 8.0e-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 3.579142895742635e-207 estimated_step_error 3.579142895742635e-207 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 2.45957066268617e-196 estimated_step_error 2.45957066268617e-196 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 1.6902073784087134e-185 estimated_step_error 1.6902073784087134e-185 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 1.161506186669873e-174 estimated_step_error 1.161506186669873e-174 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 7.981871867007481e-164 estimated_step_error 7.981871867007481e-164 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 5.485185973080913e-153 estimated_step_error 5.485185973080913e-153 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 3.76950846651465e-142 estimated_step_error 3.76950846651465e-142 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 2.590547817884198e-131 estimated_step_error 2.590547817884198e-131 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 1.7804326687478784e-120 estimated_step_error 1.7804326687478784e-120 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 1.2238089172282164e-109 estimated_step_error 1.2238089172282164e-109 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 8.414144536547605e-99 estimated_step_error 8.414144536547605e-99 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 5.787928474968382e-88 estimated_step_error 5.787928474968382e-88 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 3.9853913168419785e-77 estimated_step_error 3.9853913168419785e-77 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 2.749741324285062e-66 estimated_step_error 2.749741324285062e-66 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 1.904906640413075e-55 estimated_step_error 1.904906640413075e-55 best_h 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] 2.0 y[1] (analytic) 0.0625 y[1] (numeric) 0.0625 absolute error 0.0 relative error 0.0% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 4.0 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9969992498124536 Order of pole (three term test) 1225.0262565641412 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.01 y[1] (analytic) 0.06281367579349376 y[1] (numeric) 0.06281367579349373 absolute error 2.7755575615628914e-17 relative error 4.4187153935837386e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 3.99 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.1146875 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9870067516879217 Order of pole (three term test) 1225.026256564141 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0199999999999996 y[1] (analytic) 0.06312971894649123 y[1] (numeric) 0.06312971894649119 absolute error 4.163336342344337e-17 relative error 6.594891299727125e-14% Correct digits 16 h 0.01 Radius of convergence (given) for eq 1 3.9800000000000004 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.104375 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9770142535634307 Order of pole (three term test) 1225.026256564153 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0299999999999994 y[1] (analytic) 0.06344815334149698 y[1] (numeric) 0.06344815334149691 absolute error 6.938893903907228e-17 relative error 1.0936321293009147e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.9700000000000006 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.094062500000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9670217554388505 Order of pole (three term test) 1225.026256564138 Radius of convergence (six term test) for eq 1 1.7350028707701777 Order of pole (six term test) 4.877520609625208e-11 TOP MAIN SOLVE Loop x[1] 2.039999999999999 y[1] (analytic) 0.06376900316294254 y[1] (numeric) 0.06376900316294244 absolute error 9.71445146547012e-17 relative error 1.5233814210091627e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.960000000000001 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.083750000000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9570292573143515 Order of pole (three term test) 1225.026256564148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.049999999999999 y[1] (analytic) 0.06409229290177852 y[1] (numeric) 0.06409229290177841 absolute error 1.1102230246251565e-16 relative error 1.7322254741714015e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.950000000000001 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.073437500000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9470367591898072 Order of pole (three term test) 1225.0262565641438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0599999999999987 y[1] (analytic) 0.06441804736014838 y[1] (numeric) 0.06441804736014824 absolute error 1.3877787807814457e-16 relative error 2.1543322681338866e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.9400000000000013 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.063125000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9370442610652554 Order of pole (three term test) 1225.0262565641372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.0699999999999985 y[1] (analytic) 0.06474629165614534 y[1] (numeric) 0.06474629165614518 absolute error 1.6653345369377348e-16 relative error 2.572092538954964e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.9300000000000015 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.052812500000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9270517629407724 Order of pole (three term test) 1225.0262565641522 Radius of convergence (six term test) for eq 1 14.991225959486652 Order of pole (six term test) 7.876366225900711e-10 TOP MAIN SOLVE Loop x[1] 2.0799999999999983 y[1] (analytic) 0.06507705122865468 y[1] (numeric) 0.06507705122865448 absolute error 1.942890293094024e-16 relative error 2.9855229399800034e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.9200000000000017 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.042500000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.9170592648162303 Order of pole (three term test) 1225.026256564149 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.089999999999998 y[1] (analytic) 0.06541035184228249 y[1] (numeric) 0.06541035184228228 absolute error 2.0816681711721685e-16 relative error 3.1824751167697267e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.910000000000002 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.032187500000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.907066766691727 Order of pole (three term test) 1225.0262565641578 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.099999999999998 y[1] (analytic) 0.06574621959237337 y[1] (numeric) 0.06574621959237312 absolute error 2.498001805406602e-16 relative error 3.799460746023446e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.900000000000002 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.021875000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.897074268567198 Order of pole (three term test) 1225.0262565641583 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1099999999999977 y[1] (analytic) 0.06608468091011814 y[1] (numeric) 0.06608468091011786 absolute error 2.7755575615628914e-16 relative error 4.2000014577325885e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8900000000000023 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.011562500000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.887081770442681 Order of pole (three term test) 1225.0262565641628 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1199999999999974 y[1] (analytic) 0.06642576256775419 y[1] (numeric) 0.06642576256775387 absolute error 3.191891195797325e-16 relative error 4.805200681801131e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8800000000000026 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 4.001250000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8770892723180923 Order of pole (three term test) 1225.0262565641444 Radius of convergence (six term test) for eq 1 4.874160915787862 Order of pole (six term test) 4.602540570886049e-11 TOP MAIN SOLVE Loop x[1] 2.1299999999999972 y[1] (analytic) 0.06676949168385972 y[1] (numeric) 0.06676949168385936 absolute error 3.608224830031759e-16 relative error 5.404002245690272e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8700000000000028 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.9909375000000034 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8670967741935525 Order of pole (three term test) 1225.0262565641417 Radius of convergence (six term test) for eq 1 2.2553160696829595 Order of pole (six term test) 1.7905676941154525e-11 TOP MAIN SOLVE Loop x[1] 2.139999999999997 y[1] (analytic) 0.0671158957287443 y[1] (numeric) 0.06711589572874391 absolute error 3.885780586188048e-16 relative error 5.789657642196753e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.860000000000003 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.980625000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8571042760690264 Order of pole (three term test) 1225.0262565641428 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.149999999999997 y[1] (analytic) 0.06746500252993749 y[1] (numeric) 0.06746500252993706 absolute error 4.3021142204224816e-16 relative error 6.376808803221233e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.850000000000003 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.970312500000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8471117779445345 Order of pole (three term test) 1225.0262565641553 Radius of convergence (six term test) for eq 1 1.841499917917043 Order of pole (six term test) 7.119638212316204e-11 TOP MAIN SOLVE Loop x[1] 2.1599999999999966 y[1] (analytic) 0.06781684027777765 y[1] (numeric) 0.06781684027777721 absolute error 4.440892098500626e-16 relative error 6.548361852765095e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8400000000000034 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.960000000000003 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.83711927981997 Order of pole (three term test) 1225.026256564145 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1699999999999964 y[1] (analytic) 0.0681714375311031 y[1] (numeric) 0.06817143753110261 absolute error 4.85722573273506e-16 relative error 7.125015855091745e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8300000000000036 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.9496875000000045 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8271267816954007 Order of pole (three term test) 1225.0262565641324 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.179999999999996 y[1] (analytic) 0.06852882322304747 y[1] (numeric) 0.06852882322304696 absolute error 5.134781488891349e-16 relative error 7.492878539849828e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.820000000000004 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.9393750000000036 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8171342835708866 Order of pole (three term test) 1225.026256564138 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.189999999999996 y[1] (analytic) 0.06888902666694208 y[1] (numeric) 0.06888902666694152 absolute error 5.551115123125783e-16 relative error 8.058054223880635e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.810000000000004 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.929062500000004 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.8071417854464054 Order of pole (three term test) 1225.0262565641542 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.1999999999999957 y[1] (analytic) 0.06925207756232672 y[1] (numeric) 0.06925207756232613 absolute error 5.967448757360216e-16 relative error 8.616996005628171e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.8000000000000043 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.9187500000000046 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.79714928732186 Order of pole (three term test) 1225.0262565641497 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2099999999999955 y[1] (analytic) 0.06961800600107194 y[1] (numeric) 0.06961800600107132 absolute error 6.245004513516506e-16 relative error 8.970386933260266e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.7900000000000045 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.908437500000004 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.787156789197281 Order of pole (three term test) 1225.0262565641335 Radius of convergence (six term test) for eq 1 2.8785058754875905 Order of pole (six term test) 3.5001335163542535e-11 TOP MAIN SOLVE Loop x[1] 2.2199999999999953 y[1] (analytic) 0.06998684247361478 y[1] (numeric) 0.06998684247361411 absolute error 6.661338147750939e-16 relative error 9.517986399032477e-13% Correct digits 15 h 0.01 Radius of convergence (given) for eq 1 3.7800000000000047 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8981250000000043 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.7771642910727725 Order of pole (three term test) 1225.0262565641408 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.229999999999995 y[1] (analytic) 0.07035861787531027 y[1] (numeric) 0.07035861787530956 absolute error 7.077671781985373e-16 relative error 1.0059424127018018e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.770000000000005 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.887812500000005 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.767171792948238 Order of pole (three term test) 1225.0262565641399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.239999999999995 y[1] (analytic) 0.07073336351290158 y[1] (numeric) 0.07073336351290081 absolute error 7.632783294297951e-16 relative error 1.07909237101467e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.760000000000005 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8775000000000053 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.7571792948237586 Order of pole (three term test) 1225.0262565641567 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2499999999999947 y[1] (analytic) 0.0711111111111109 y[1] (numeric) 0.07111111111111011 absolute error 7.91033905045424e-16 relative error 1.1123914289701308e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.7500000000000053 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.867187500000005 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.747186796699244 Order of pole (three term test) 1225.0262565641622 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2599999999999945 y[1] (analytic) 0.07149189281935409 y[1] (numeric) 0.07149189281935324 absolute error 8.465450562766819e-16 relative error 1.1841133629175748e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.7400000000000055 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8568750000000054 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.737194298574654 Order of pole (three term test) 1225.0262565641426 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.2699999999999942 y[1] (analytic) 0.07187574121858109 y[1] (numeric) 0.07187574121858022 absolute error 8.743006318923108e-16 relative error 1.216405726145457e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.7300000000000058 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.846562500000006 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.7272018004501173 Order of pole (three term test) 1225.0262565641406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.279999999999994 y[1] (analytic) 0.07226268932824581 y[1] (numeric) 0.07226268932824488 absolute error 9.298117831235686e-16 relative error 1.2867107379577232e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.720000000000006 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8362500000000055 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.7172093023255597 Order of pole (three term test) 1225.026256564132 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.289999999999994 y[1] (analytic) 0.0726527706134071 y[1] (numeric) 0.07265277061340612 absolute error 9.71445146547012e-16 relative error 1.3371068141587774e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.710000000000006 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8259375000000073 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.7072168042010842 Order of pole (three term test) 1225.0262565641506 Radius of convergence (six term test) for eq 1 13.79097997073329 Order of pole (six term test) 1.3638157270179363e-09 TOP MAIN SOLVE Loop x[1] 2.2999999999999936 y[1] (analytic) 0.07304601899196468 y[1] (numeric) 0.07304601899196365 absolute error 1.0269562977782698e-15 relative error 1.4059031716584562e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.7000000000000064 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.8156250000000065 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.697224306076556 Order of pole (three term test) 1225.0262565641513 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3099999999999934 y[1] (analytic) 0.07344246884203233 y[1] (numeric) 0.07344246884203125 absolute error 1.0824674490095276e-15 relative error 1.4738985032458682e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6900000000000066 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.805312500000007 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6872318079520046 Order of pole (three term test) 1225.0262565641447 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.319999999999993 y[1] (analytic) 0.07384215500945152 y[1] (numeric) 0.07384215500945039 absolute error 1.124100812432971e-15 relative error 1.5223022842292323e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.680000000000007 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.795000000000007 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6772393098274456 Order of pole (three term test) 1225.026256564135 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.329999999999993 y[1] (analytic) 0.07424511281544864 y[1] (numeric) 0.07424511281544746 absolute error 1.1796119636642288e-15 relative error 1.5888075577397191e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.670000000000007 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7846875000000075 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6672468117029813 Order of pole (three term test) 1225.0262565641576 Radius of convergence (six term test) for eq 1 3.0655123912809077 Order of pole (six term test) 8.480682822664676e-11 TOP MAIN SOLVE Loop x[1] 2.3399999999999928 y[1] (analytic) 0.07465137806443878 y[1] (numeric) 0.07465137806443754 absolute error 1.2351231148954867e-15 relative error 1.6545215197894045e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6600000000000072 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7743750000000076 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6572543135783917 Order of pole (three term test) 1225.0262565641378 Radius of convergence (six term test) for eq 1 2.2564964463620756 Order of pole (six term test) 4.4007464339301805e-11 TOP MAIN SOLVE Loop x[1] 2.3499999999999925 y[1] (analytic) 0.07506098705197943 y[1] (numeric) 0.07506098705197814 absolute error 1.2906342661267445e-15 relative error 1.7194475010473622e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6500000000000075 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7640625000000076 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6472618154539 Order of pole (three term test) 1225.0262565641508 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3599999999999923 y[1] (analytic) 0.07547397657287735 y[1] (numeric) 0.07547397657287601 absolute error 1.3461454173580023e-15 relative error 1.7835888321826661e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6400000000000077 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7537500000000077 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6372693173294217 Order of pole (three term test) 1225.0262565641688 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.369999999999992 y[1] (analytic) 0.07589038392945197 y[1] (numeric) 0.07589038392945056 absolute error 1.4016565685892601e-15 relative error 1.8469488438643903e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.630000000000008 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7434375000000077 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.627276819204811 Order of pole (three term test) 1225.0262565641415 Radius of convergence (six term test) for eq 1 2.450182562494997 Order of pole (six term test) 5.140776693224325e-12 TOP MAIN SOLVE Loop x[1] 2.379999999999992 y[1] (analytic) 0.07631024693995876 y[1] (numeric) 0.07631024693995729 absolute error 1.4710455076283324e-15 relative error 1.9277168750164806e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.620000000000008 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.733125000000009 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.6172843210802768 Order of pole (three term test) 1225.0262565641406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3899999999999917 y[1] (analytic) 0.07673360394717624 y[1] (numeric) 0.07673360394717471 absolute error 1.5265566588595902e-15 relative error 1.9894239033924156e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6100000000000083 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7228125000000083 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.607291822955752 Order of pole (three term test) 1225.0262565641426 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.3999999999999915 y[1] (analytic) 0.07716049382716013 y[1] (numeric) 0.07716049382715855 absolute error 1.582067810090848e-15 relative error 2.0503598818777488e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.6000000000000085 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.712500000000009 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5972993248312 Order of pole (three term test) 1225.0262565641356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4099999999999913 y[1] (analytic) 0.07759095599816848 y[1] (numeric) 0.07759095599816683 absolute error 1.6514567491299204e-15 relative error 2.128413972846143e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5900000000000087 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.7021875000000093 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5873068267066817 Order of pole (three term test) 1225.0262565641399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.419999999999991 y[1] (analytic) 0.07802503042976149 y[1] (numeric) 0.07802503042975976 absolute error 1.7208456881689926e-15 relative error 2.2055046677849184e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.580000000000009 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6918750000000085 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5773143285821845 Order of pole (three term test) 1225.0262565641515 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.429999999999991 y[1] (analytic) 0.07846275765208004 y[1] (numeric) 0.07846275765207826 absolute error 1.7763568394002505e-15 relative error 2.263949028247237e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.570000000000009 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6815625000000094 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.567321830457659 Order of pole (three term test) 1225.0262565641535 Radius of convergence (six term test) for eq 1 5.259468142069826 Order of pole (six term test) 2.823199451995606e-10 TOP MAIN SOLVE Loop x[1] 2.4399999999999906 y[1] (analytic) 0.07890417876530699 y[1] (numeric) 0.07890417876530516 absolute error 1.8318679906315083e-15 relative error 2.3216362166067607e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5600000000000094 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.67125000000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.557329332333113 Order of pole (three term test) 1225.0262565641483 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4499999999999904 y[1] (analytic) 0.07934933544931519 y[1] (numeric) 0.07934933544931327 absolute error 1.915134717478395e-15 relative error 2.4135485277021603e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5500000000000096 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6609375000000095 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5473368342086022 Order of pole (three term test) 1225.0262565641553 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.45999999999999 y[1] (analytic) 0.07979826997350653 y[1] (numeric) 0.07979826997350456 absolute error 1.970645868709653e-15 relative error 2.4695345768322023e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.54000000000001 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6506250000000096 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5373443360840278 Order of pole (three term test) 1225.0262565641399 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.46999999999999 y[1] (analytic) 0.08025102520684656 y[1] (numeric) 0.08025102520684452 absolute error 2.040034807748725e-15 relative error 2.5420669735876236e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.53000000000001 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6403125000000105 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5273518379595434 Order of pole (three term test) 1225.0262565641565 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4799999999999898 y[1] (analytic) 0.08070764462809871 y[1] (numeric) 0.08070764462809658 absolute error 2.123301534595612e-15 relative error 2.6308555334253622e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5200000000000102 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.6300000000000106 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5173593398349534 Order of pole (three term test) 1225.0262565641356 Radius of convergence (six term test) for eq 1 6.2219775230064895 Order of pole (six term test) -4.203570824756753e-11 TOP MAIN SOLVE Loop x[1] 2.4899999999999896 y[1] (analytic) 0.08116817233626303 y[1] (numeric) 0.08116817233626082 absolute error 2.2065682614424986e-15 relative error 2.718514163779789e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5100000000000104 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.61968750000001 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.5073668417104367 Order of pole (three term test) 1225.0262565641406 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.4999999999999893 y[1] (analytic) 0.081632653061224 y[1] (numeric) 0.08163265306122172 absolute error 2.275957200481571e-15 relative error 2.7880475705899413e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.5000000000000107 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.609375000000011 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.4973743435859235 Order of pole (three term test) 1225.0262565641467 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.509999999999989 y[1] (analytic) 0.08210113217461218 y[1] (numeric) 0.08210113217460982 absolute error 2.3592239273284576e-15 relative error 2.8735583357253526e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.490000000000011 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.599062500000011 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.487381845461397 Order of pole (three term test) 1225.0262565641485 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.519999999999989 y[1] (analytic) 0.08257365570088467 y[1] (numeric) 0.08257365570088222 absolute error 2.4424906541753444e-15 relative error 2.9579538818325278e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.480000000000011 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.588750000000011 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.477389347336884 Order of pole (three term test) 1225.0262565641547 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5299999999999887 y[1] (analytic) 0.08305027032862938 y[1] (numeric) 0.08305027032862686 absolute error 2.525757381022231e-15 relative error 3.0412392049150777e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.4700000000000113 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.5784375000000117 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.467396849212326 Order of pole (three term test) 1225.0262565641453 Radius of convergence (six term test) for eq 1 5.345839392584406 Order of pole (six term test) 3.822719918389339e-11 TOP MAIN SOLVE Loop x[1] 2.5399999999999885 y[1] (analytic) 0.08353102342209841 y[1] (numeric) 0.0835310234220958 absolute error 2.609024107869118e-15 relative error 3.123419300976614e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.4600000000000115 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.5681250000000118 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.457404351087822 Order of pole (three term test) 1225.026256564155 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5499999999999883 y[1] (analytic) 0.08401596303297569 y[1] (numeric) 0.084015963032973 absolute error 2.6922908347160046e-15 relative error 3.2044991660207463e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.4500000000000117 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.557812500000012 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.4474118529632887 Order of pole (three term test) 1225.026256564154 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.559999999999988 y[1] (analytic) 0.0845051379123845 y[1] (numeric) 0.0845051379123817 absolute error 2.789435349370706e-15 relative error 3.300906215031341e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.440000000000012 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.5475000000000128 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.43741935483875 Order of pole (three term test) 1225.0262565641517 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.569999999999988 y[1] (analytic) 0.08499859752314026 y[1] (numeric) 0.08499859752313739 absolute error 2.8727020762175925e-15 relative error 3.3797052656492596e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.430000000000012 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.537187500000012 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.4274268567142343 Order of pole (three term test) 1225.0262565641567 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.5799999999999876 y[1] (analytic) 0.08549639205225477 y[1] (numeric) 0.0854963920522518 absolute error 2.9698465908722937e-15 relative error 3.473651366547895e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.4200000000000124 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.526875000000012 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.417434358589658 Order of pole (three term test) 1225.02625656414 Radius of convergence (six term test) for eq 1 5.422003538209845 Order of pole (six term test) -3.879208065882267e-11 TOP MAIN SOLVE Loop x[1] 2.5899999999999874 y[1] (analytic) 0.08599857242369713 y[1] (numeric) 0.08599857242369406 absolute error 3.066991105526995e-15 relative error 3.5663279274178714e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.4100000000000126 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.5165625000000125 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.4074418604651417 Order of pole (three term test) 1225.026256564146 Radius of convergence (six term test) for eq 1 0.4691319940882478 Order of pole (six term test) 3.360867140145274e-11 TOP MAIN SOLVE Loop x[1] 2.599999999999987 y[1] (analytic) 0.08650519031141804 y[1] (numeric) 0.08650519031141486 absolute error 3.1780134079895106e-15 relative error 3.673783499635902e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.400000000000013 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.506250000000013 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.397449362340652 Order of pole (three term test) 1225.0262565641608 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.609999999999987 y[1] (analytic) 0.08701629815264333 y[1] (numeric) 0.08701629815264005 absolute error 3.2890357104520263e-15 relative error 3.779792728808602e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.390000000000013 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4959375000000135 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.387456864216086 Order of pole (three term test) 1225.026256564148 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.619999999999987 y[1] (analytic) 0.08753194916144325 y[1] (numeric) 0.08753194916143986 absolute error 3.3861802251067274e-15 relative error 3.86850773637096e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.380000000000013 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.485625000000014 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.377464366091539 Order of pole (three term test) 1225.0262565641424 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6299999999999866 y[1] (analytic) 0.08805219734258397 y[1] (numeric) 0.08805219734258049 absolute error 3.4833247397614286e-15 relative error 3.9559770736996884e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.3700000000000134 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4753125000000145 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.367471867967045 Order of pole (three term test) 1225.0262565641558 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6399999999999864 y[1] (analytic) 0.08857709750566821 y[1] (numeric) 0.08857709750566461 absolute error 3.594347042223944e-15 relative error 4.0578740367891775e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.3600000000000136 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.465000000000014 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.3574793698424936 Order of pole (three term test) 1225.0262565641483 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.649999999999986 y[1] (analytic) 0.08910670527957154 y[1] (numeric) 0.08910670527956784 absolute error 3.70536934468646e-15 relative error 4.1583507470744144e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.350000000000014 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4546875000000137 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.347486871717971 Order of pole (three term test) 1225.0262565641513 Radius of convergence (six term test) for eq 1 4.3982744984433015 Order of pole (six term test) 1.8733814499682921e-10 TOP MAIN SOLVE Loop x[1] 2.659999999999986 y[1] (analytic) 0.08964107712718201 y[1] (numeric) 0.08964107712717817 absolute error 3.8441472227646045e-15 relative error 4.288376875827318e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.340000000000014 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4443750000000146 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.337494373593444 Order of pole (three term test) 1225.026256564153 Radius of convergence (six term test) for eq 1 5.642804438782788 Order of pole (six term test) 2.3637980461899133e-10 TOP MAIN SOLVE Loop x[1] 2.6699999999999857 y[1] (analytic) 0.09018027036044977 y[1] (numeric) 0.09018027036044582 absolute error 3.95516952522712e-15 relative error 4.385847934829139e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.3300000000000143 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.434062500000015 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.3275018754688745 Order of pole (three term test) 1225.0262565641387 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6799999999999855 y[1] (analytic) 0.09072434315575477 y[1] (numeric) 0.09072434315575069 absolute error 4.08006961549745e-15 relative error 4.497215932985948e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.3200000000000145 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4237500000000147 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.317509377344373 Order of pole (three term test) 1225.0262565641494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.6899999999999853 y[1] (analytic) 0.09127335456959969 y[1] (numeric) 0.0912733545695955 absolute error 4.191091917959966e-15 relative error 4.591802216236159e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.3100000000000147 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.4134375000000152 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.307516879219827 Order of pole (three term test) 1225.0262565641438 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.699999999999985 y[1] (analytic) 0.09182736455463644 y[1] (numeric) 0.09182736455463214 absolute error 4.3021142204224816e-15 relative error 4.685002386040125e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.300000000000015 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.403125000000016 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.29752438109529 Order of pole (three term test) 1225.0262565641417 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.709999999999985 y[1] (analytic) 0.0923864339760341 y[1] (numeric) 0.09238643397602966 absolute error 4.440892098500626e-15 relative error 4.806866016338107e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.290000000000015 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3928125000000153 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2875318829708147 Order of pole (three term test) 1225.0262565641626 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7199999999999847 y[1] (analytic) 0.09295062462819663 y[1] (numeric) 0.09295062462819205 absolute error 4.579669976578771e-15 relative error 4.926992147602551e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.2800000000000153 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3825000000000154 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2775393848462615 Order of pole (three term test) 1225.0262565641542 Radius of convergence (six term test) for eq 1 1.7906686268292225 Order of pole (six term test) 6.377476324814779e-11 TOP MAIN SOLVE Loop x[1] 2.7299999999999844 y[1] (analytic) 0.09351999925183911 y[1] (numeric) 0.0935199992518344 absolute error 4.718447854656915e-15 relative error 5.045389106506141e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.2700000000000156 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.372187500000016 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2675468867216813 Order of pole (three term test) 1225.0262565641356 Radius of convergence (six term test) for eq 1 3.337842086368971 Order of pole (six term test) -6.553335651915404e-11 TOP MAIN SOLVE Loop x[1] 2.7399999999999842 y[1] (analytic) 0.09409462155143121 y[1] (numeric) 0.09409462155142634 absolute error 4.871103520542874e-15 relative error 5.176813977492195e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.2600000000000158 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.361875000000017 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2575543885971556 Order of pole (three term test) 1225.0262565641376 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.749999999999984 y[1] (analytic) 0.09467455621301682 y[1] (numeric) 0.09467455621301181 absolute error 5.009881398621019e-15 relative error 5.291687227293503e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.250000000000016 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3515625000000164 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.247561890472677 Order of pole (three term test) 1225.0262565641574 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.759999999999984 y[1] (analytic) 0.09525986892241942 y[1] (numeric) 0.09525986892241425 absolute error 5.162537064506978e-15 relative error 5.419424908836899e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.240000000000016 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3412500000000165 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2375693923481608 Order of pole (three term test) 1225.026256564163 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7699999999999836 y[1] (analytic) 0.09585062638384244 y[1] (numeric) 0.09585062638383714 absolute error 5.3013149425851225e-15 relative error 5.530808866449689e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.2300000000000164 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3309375000000174 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2275768942235707 Order of pole (three term test) 1225.0262565641408 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.7799999999999834 y[1] (analytic) 0.09644689633887482 y[1] (numeric) 0.09644689633886935 absolute error 5.467848396278896e-15 relative error 5.669283931197869e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.2200000000000166 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.3206250000000166 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2175843960990314 Order of pole (three term test) 1225.0262565641372 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.789999999999983 y[1] (analytic) 0.0970487475859114 y[1] (numeric) 0.09704874758590576 absolute error 5.6343818499726694e-15 relative error 5.805723402030398e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.210000000000017 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.310312500000017 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.2075918979745586 Order of pole (three term test) 1225.0262565641597 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.799999999999983 y[1] (analytic) 0.09765624999999896 y[1] (numeric) 0.09765624999999317 absolute error 5.7870375158586285e-15 relative error 5.9259264162392986e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.200000000000017 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.300000000000018 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1975993998499663 Order of pole (three term test) 1225.0262565641362 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8099999999999827 y[1] (analytic) 0.0982694745531185 y[1] (numeric) 0.09826947455311254 absolute error 5.9674487573602164e-15 relative error 6.072535529977395e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1900000000000173 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2896875000000176 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1876069017254616 Order of pole (three term test) 1225.0262565641463 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8199999999999825 y[1] (analytic) 0.09888849333491447 y[1] (numeric) 0.09888849333490833 absolute error 6.13398221105399e-15 relative error 6.202928171106305e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1800000000000175 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2793750000000186 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.177614403600899 Order of pole (three term test) 1225.0262565641337 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8299999999999823 y[1] (analytic) 0.09951337957388261 y[1] (numeric) 0.09951337957387629 absolute error 6.314393452555578e-15 relative error 6.345270836538645e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1700000000000177 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2690625000000186 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1676219054763863 Order of pole (three term test) 1225.0262565641408 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.839999999999982 y[1] (analytic) 0.10014420765902786 y[1] (numeric) 0.10014420765902138 absolute error 6.480926906249351e-15 relative error 6.471594371504426e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.160000000000018 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2587500000000182 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1576294073518802 Order of pole (three term test) 1225.0262565641506 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.849999999999982 y[1] (analytic) 0.10078105316200438 y[1] (numeric) 0.1007810531619977 absolute error 6.675215935558754e-15 relative error 6.62348301205825e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.150000000000018 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2484375000000187 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.147636909227316 Order of pole (three term test) 1225.0262565641376 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8599999999999817 y[1] (analytic) 0.10142399285974972 y[1] (numeric) 0.10142399285974284 absolute error 6.8833827526759706e-15 relative error 6.786740058828479e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1400000000000183 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.238125000000019 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1376444111027797 Order of pole (three term test) 1225.0262565641356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8699999999999815 y[1] (analytic) 0.1020731047576262 y[1] (numeric) 0.10207310475761912 absolute error 7.077671781985373e-15 relative error 6.933924268093333e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1300000000000185 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2278125000000193 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1276519129782843 Order of pole (three term test) 1225.0262565641494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.8799999999999812 y[1] (analytic) 0.10272846811308227 y[1] (numeric) 0.10272846811307497 absolute error 7.299716386910404e-15 relative error 7.105835919674149e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.1200000000000188 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2175000000000193 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.1176594148537182 Order of pole (three term test) 1225.0262565641356 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.889999999999981 y[1] (analytic) 0.10339016345984718 y[1] (numeric) 0.10339016345983966 absolute error 7.521760991835436e-15 relative error 7.27512244891324e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.110000000000019 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.2071875000000194 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.107666916729201 Order of pole (three term test) 1225.026256564141 Radius of convergence (six term test) for eq 1 3.142802525947088 Order of pole (six term test) 9.351452945338679e-11 TOP MAIN SOLVE Loop x[1] 2.899999999999981 y[1] (analytic) 0.104058272632673 y[1] (numeric) 0.10405827263266529 absolute error 7.716050021144838e-15 relative error 7.415124070320281e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.100000000000019 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.19687500000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.097674418604692 Order of pole (three term test) 1225.0262565641494 Radius of convergence (six term test) for eq 1 3.696991139403368 Order of pole (six term test) 1.2733991638924635e-10 TOP MAIN SOLVE Loop x[1] 2.9099999999999806 y[1] (analytic) 0.10473287879263807 y[1] (numeric) 0.10473287879263012 absolute error 7.951972413877684e-15 relative error 7.592622780494647e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0900000000000194 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.1865625000000204 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.087681920480152 Order of pole (three term test) 1225.0262565641463 Radius of convergence (six term test) for eq 1 23.648369122077252 Order of pole (six term test) 2.4080506477730523e-09 TOP MAIN SOLVE Loop x[1] 2.9199999999999804 y[1] (analytic) 0.10541406645302616 y[1] (numeric) 0.10541406645301798 absolute error 8.174017018802715e-15 relative error 7.754199504717106e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0800000000000196 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.17625000000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.077689422355601 Order of pole (three term test) 1225.0262565641383 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.92999999999998 y[1] (analytic) 0.10610192150579711 y[1] (numeric) 0.1061019215057887 absolute error 8.409939411535561e-15 relative error 7.926283795978252e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.07000000000002 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.16593750000002 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.06769692423109 Order of pole (three term test) 1225.0262565641463 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.93999999999998 y[1] (analytic) 0.10679653124866363 y[1] (numeric) 0.10679653124865501 absolute error 8.618106228652778e-15 relative error 8.069649948261422e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.06000000000002 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.1556250000000206 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.057704426106519 Order of pole (three term test) 1225.0262565641299 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9499999999999797 y[1] (analytic) 0.10749798441279083 y[1] (numeric) 0.10749798441278195 absolute error 8.881784197001252e-15 relative error 8.262279749260525e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0500000000000203 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.1453125000000206 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.047711927982027 Order of pole (three term test) 1225.0262565641456 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9599999999999795 y[1] (analytic) 0.10820637119113428 y[1] (numeric) 0.10820637119112514 absolute error 9.145462165349727e-15 relative error 8.451870314729718e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0400000000000205 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.135000000000021 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.0377194298574497 Order of pole (three term test) 1225.0262565641265 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9699999999999793 y[1] (analytic) 0.10892178326743415 y[1] (numeric) 0.10892178326742477 absolute error 9.381384558082573e-15 relative error 8.612955348930148e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0300000000000207 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.1246875000000216 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.0277269317329885 Order of pole (three term test) 1225.0262565641551 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.979999999999979 y[1] (analytic) 0.10964431384588243 y[1] (numeric) 0.10964431384587277 absolute error 9.658940314238862e-15 relative error 8.809339924198534e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.020000000000021 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.114375000000021 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.017734433608446 Order of pole (three term test) 1225.0262565641506 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.989999999999979 y[1] (analytic) 0.110374057681481 y[1] (numeric) 0.11037405768147106 absolute error 9.936496070395151e-15 relative error 9.002564804738837e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.010000000000021 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.104062500000022 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 3.007741935483912 Order of pole (three term test) 1225.0262565641494 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] 2.9999999999999787 y[1] (analytic) 0.11111111111110954 y[1] (numeric) 0.11111111111109931 absolute error 1.0227929614359255e-14 relative error 9.20513665292346e-12% Correct digits 14 h 0.01 Radius of convergence (given) for eq 1 3.0000000000000213 Order of pole (given) 3.0 Radius of convergence (ratio test) for eq 1 3.0937500000000218 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 2.9977494373593485 Order of pole (three term test) 1225.0262565641358 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = m1 * 2.0 / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0) ; Iterations 101 Total Elapsed Time 0.0 Seconds Elapsed Time(since restart) 0.0 Seconds Time to Timeout 3 Minutes 0.0 Seconds Percent Done 101.99999999999783%