##############ECHO OF PROBLEM################# ##############temp/diff0postode.ode################# diff ( y , x , 1 ) = y; ! // BEGIN FIRST INPUT BLOCK Digits=32; max_terms=30; ! // END FIRST INPUT BLOCK // BEGIN SECOND INPUT BLOCK x_start=-5.0; x_end=5.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=false; 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=0.1; 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(exp(x)); } // 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 = 10 estimated_steps = 10000000 step_error = 1e-17 est_needed_step_err = 1e-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 = 1.670738851013513e-185 estimated_step_error = 1.670738851013513e-185 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 = 1.121213884085041e-177 estimated_step_error = 1.121213884085041e-177 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 = 7.524339284876722e-170 estimated_step_error = 7.524339284876722e-170 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 = 5.049498991623479e-162 estimated_step_error = 5.049498991623479e-162 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 = 3.388661912994025e-154 estimated_step_error = 3.388661912994025e-154 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 = 2.274093188416526e-146 estimated_step_error = 2.274093188416526e-146 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 = 1.526119009415009e-138 estimated_step_error = 1.526119009415009e-138 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 = 1.024162344329788e-130 estimated_step_error = 1.024162344329788e-130 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 = 6.873053439671597e-123 estimated_step_error = 6.873053439671597e-123 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 = 4.61244995199849e-115 estimated_step_error = 4.61244995199849e-115 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 = 3.095392114506185e-107 estimated_step_error = 3.095392114506185e-107 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 = 2.077321877235378e-99 estimated_step_error = 2.077321877235378e-99 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 = 1.394119988517542e-91 estimated_step_error = 1.394119988517542e-91 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 = 9.356490626093137e-84 estimated_step_error = 9.356490626093137e-84 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 = 6.279987395703641e-76 estimated_step_error = 6.279987395703641e-76 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 = 4.215707623357401e-68 estimated_step_error = 4.215707623357401e-68 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 = 2.830832213653079e-60 estimated_step_error = 2.830832213653079e-60 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 = 1.902050207024072e-52 estimated_step_error = 1.902050207024072e-52 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = -5 y[1] (analytic) = 0.006737946999085467 y[1] (numeric) = 0.006737946999085467 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.7 Radius of convergence (three term test) for eq 1 = 7.625e+15 Order of pole (three term test) = 7.625e+15 Derivative of radius w.r.t nth term = 9.387e+88 Derivative of order w.r.t nth term = -9.387e+88 Derivative of radius w.r.t (n-1)th term = 6.954e+86 Derivative of order w.r.t (n-1)th term = 3.554e+87 Derivative of radius w.r.t (n-2)th term = -1.337e+84 Derivative of order w.r.t (n-2)th term = -1.651e+195 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.162e+32 Guess error in order = -1.743e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.9 y[1] (analytic) = 0.007446583070924338 y[1] (numeric) = 0.007446583070924341 absolute error = 2.602085213965211e-18 relative error = 3.494334501048164e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.7 Radius of convergence (three term test) for eq 1 = 1.043e+16 Order of pole (three term test) = 1.043e+16 Derivative of radius w.r.t nth term = 1.593e+89 Derivative of order w.r.t nth term = -1.593e+89 Derivative of radius w.r.t (n-1)th term = 1.18e+87 Derivative of order w.r.t (n-1)th term = 6.031e+87 Derivative of radius w.r.t (n-2)th term = -2.269e+84 Derivative of order w.r.t (n-2)th term = -2.294e+195 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.179e+32 Guess error in order = -3.268e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.800000000000001 y[1] (analytic) = 0.008229747049020023 y[1] (numeric) = 0.008229747049020028 absolute error = 5.204170427930421e-18 relative error = 6.323609215364792e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.7 Radius of convergence (three term test) for eq 1 = 7.914e+15 Order of pole (three term test) = 7.914e+15 Derivative of radius w.r.t nth term = 8.287e+88 Derivative of order w.r.t nth term = -8.287e+88 Derivative of radius w.r.t (n-1)th term = 6.138e+86 Derivative of order w.r.t (n-1)th term = 3.137e+87 Derivative of radius w.r.t (n-2)th term = -1.18e+84 Derivative of order w.r.t (n-2)th term = -9.769e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.253e+32 Guess error in order = -1.879e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.700000000000001 y[1] (analytic) = 0.009095277101695807 y[1] (numeric) = 0.009095277101695817 absolute error = 1.040834085586084e-17 relative error = 1.144367647019816e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.8 Radius of convergence (three term test) for eq 1 = 4.207e+15 Order of pole (three term test) = 4.207e+15 Derivative of radius w.r.t nth term = 2.119e+88 Derivative of order w.r.t nth term = -2.119e+88 Derivative of radius w.r.t (n-1)th term = 1.569e+86 Derivative of order w.r.t (n-1)th term = 8.022e+86 Derivative of radius w.r.t (n-2)th term = -3.018e+83 Derivative of order w.r.t (n-2)th term = -2.045e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.54e+31 Guess error in order = -5.309e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.600000000000001 y[1] (analytic) = 0.01005183574463357 y[1] (numeric) = 0.01005183574463358 absolute error = 1.561251128379126e-17 relative error = 1.553200000519946e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.8 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.500000000000002 y[1] (analytic) = 0.01110899653824229 y[1] (numeric) = 0.01110899653824231 absolute error = 2.081668171172169e-17 relative error = 1.873857970885225e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.8 Radius of convergence (three term test) for eq 1 = 5.66e+15 Order of pole (three term test) = 5.66e+15 Derivative of radius w.r.t nth term = 3.143e+88 Derivative of order w.r.t nth term = -3.143e+88 Derivative of radius w.r.t (n-1)th term = 2.328e+86 Derivative of order w.r.t (n-1)th term = 1.19e+87 Derivative of radius w.r.t (n-2)th term = -4.478e+83 Derivative of order w.r.t (n-2)th term = -2.034e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.414e+31 Guess error in order = -9.621e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.400000000000002 y[1] (analytic) = 0.01227733990306842 y[1] (numeric) = 0.01227733990306844 absolute error = 2.775557561562891e-17 relative error = 2.260715744189187e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.9 Radius of convergence (three term test) for eq 1 = 6.615e+15 Order of pole (three term test) = 6.615e+15 Derivative of radius w.r.t nth term = 3.881e+88 Derivative of order w.r.t nth term = -3.881e+88 Derivative of radius w.r.t (n-1)th term = 2.874e+86 Derivative of order w.r.t (n-1)th term = 1.469e+87 Derivative of radius w.r.t (n-2)th term = -5.528e+83 Derivative of order w.r.t (n-2)th term = -2.056e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 8.751e+31 Guess error in order = -1.313e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.300000000000002 y[1] (analytic) = 0.0135685590122009 y[1] (numeric) = 0.01356855901220093 absolute error = 3.642919299551295e-17 relative error = 2.684824008412071e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.9 Radius of convergence (three term test) for eq 1 = 2.533e+16 Order of pole (three term test) = 2.533e+16 Derivative of radius w.r.t nth term = 5.182e+89 Derivative of order w.r.t nth term = -5.182e+89 Derivative of radius w.r.t (n-1)th term = 3.839e+87 Derivative of order w.r.t (n-1)th term = 1.962e+88 Derivative of radius w.r.t (n-2)th term = -7.382e+84 Derivative of order w.r.t (n-2)th term = -2.247e+195 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.292e+33 Guess error in order = -1.937e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -4.200000000000003 y[1] (analytic) = 0.01499557682047766 y[1] (numeric) = 0.01499557682047771 absolute error = 4.510281037539698e-17 relative error = 3.007740943569805e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 125.9 Radius of convergence (three term test) for eq 1 = 4.906e+16 Order of pole (three term test) = 4.906e+16 Derivative of radius w.r.t nth term = 1.73e+90 Derivative of order w.r.t nth term = -1.73e+90 Derivative of radius w.r.t (n-1)th term = 1.282e+88 Derivative of order w.r.t (n-1)th term = 6.55e+88 Derivative of radius w.r.t (n-2)th term = -2.464e+85 Derivative of order w.r.t (n-2)th term = -6.143e+195 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.765e+33 Guess error in order = -7.148e+33 Radius of convergence (six term test) for eq 1 = 1.91e+08 Order of pole (six term test) = -7.13e+14 TOP MAIN SOLVE Loop x[1] = -4.100000000000003 y[1] (analytic) = 0.0165726754017612 y[1] (numeric) = 0.01657267540176125 absolute error = 5.551115123125783e-17 relative error = 3.349558830154762e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126 Radius of convergence (three term test) for eq 1 = 4.415e+15 Order of pole (three term test) = 4.415e+15 Derivative of radius w.r.t nth term = 1.281e+88 Derivative of order w.r.t nth term = -1.281e+88 Derivative of radius w.r.t (n-1)th term = 9.487e+85 Derivative of order w.r.t (n-1)th term = 4.849e+86 Derivative of radius w.r.t (n-2)th term = -1.824e+83 Derivative of order w.r.t (n-2)th term = -3.723e+193 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.898e+31 Guess error in order = -5.848e+31 Radius of convergence (six term test) for eq 1 = 1.355e+08 Order of pole (six term test) = -4.328e+14 TOP MAIN SOLVE Loop x[1] = -4.000000000000004 y[1] (analytic) = 0.01831563888873412 y[1] (numeric) = 0.01831563888873419 absolute error = 6.938893903907228e-17 relative error = 3.788507704295981e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126 Radius of convergence (three term test) for eq 1 = 7.469e+15 Order of pole (three term test) = 7.469e+15 Derivative of radius w.r.t nth term = 3.317e+88 Derivative of order w.r.t nth term = -3.317e+88 Derivative of radius w.r.t (n-1)th term = 2.457e+86 Derivative of order w.r.t (n-1)th term = 1.256e+87 Derivative of radius w.r.t (n-2)th term = -4.725e+83 Derivative of order w.r.t (n-2)th term = -7.894e+193 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.116e+32 Guess error in order = -1.674e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.900000000000003 y[1] (analytic) = 0.02024191144580432 y[1] (numeric) = 0.02024191144580439 absolute error = 7.632783294297951e-17 relative error = 3.770781882300968e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.800000000000003 y[1] (analytic) = 0.02237077185616552 y[1] (numeric) = 0.0223707718561656 absolute error = 7.979727989493313e-17 relative error = 3.567032930646982e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.102e+08 Order of pole (six term test) = -3.22e+14 TOP MAIN SOLVE Loop x[1] = -3.700000000000003 y[1] (analytic) = 0.02472352647033931 y[1] (numeric) = 0.0247235264703394 absolute error = 9.020562075079397e-17 relative error = 3.648574197496186e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.1 Radius of convergence (three term test) for eq 1 = 3.181e+16 Order of pole (three term test) = 3.181e+16 Derivative of radius w.r.t nth term = 4.458e+89 Derivative of order w.r.t nth term = -4.458e+89 Derivative of radius w.r.t (n-1)th term = 3.302e+87 Derivative of order w.r.t (n-1)th term = 1.688e+88 Derivative of radius w.r.t (n-2)th term = -6.35e+84 Derivative of order w.r.t (n-2)th term = -5.823e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.024e+33 Guess error in order = -3.037e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.600000000000003 y[1] (analytic) = 0.02732372244729247 y[1] (numeric) = 0.02732372244729257 absolute error = 9.71445146547012e-17 relative error = 3.555317722250078e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.1 Radius of convergence (three term test) for eq 1 = 2.619e+16 Order of pole (three term test) = 2.619e+16 Derivative of radius w.r.t nth term = 2.741e+89 Derivative of order w.r.t nth term = -2.741e+89 Derivative of radius w.r.t (n-1)th term = 2.031e+87 Derivative of order w.r.t (n-1)th term = 1.038e+88 Derivative of radius w.r.t (n-2)th term = -3.905e+84 Derivative of order w.r.t (n-2)th term = -2.932e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.376e+33 Guess error in order = -2.064e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.500000000000003 y[1] (analytic) = 0.03019738342231841 y[1] (numeric) = 0.03019738342231851 absolute error = 1.040834085586084e-16 relative error = 3.446769115819552e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.1 Radius of convergence (three term test) for eq 1 = 3.109e+16 Order of pole (three term test) = 3.109e+16 Derivative of radius w.r.t nth term = 3.531e+89 Derivative of order w.r.t nth term = -3.531e+89 Derivative of radius w.r.t (n-1)th term = 2.615e+87 Derivative of order w.r.t (n-1)th term = 1.337e+88 Derivative of radius w.r.t (n-2)th term = -5.03e+84 Derivative of order w.r.t (n-2)th term = -3.091e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.958e+33 Guess error in order = -2.937e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.400000000000003 y[1] (analytic) = 0.03337326996032598 y[1] (numeric) = 0.03337326996032609 absolute error = 1.179611963664229e-16 relative error = 3.534601089634151e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.2 Radius of convergence (three term test) for eq 1 = 4.501e+15 Order of pole (three term test) = 4.501e+15 Derivative of radius w.r.t nth term = 6.611e+87 Derivative of order w.r.t nth term = -6.611e+87 Derivative of radius w.r.t (n-1)th term = 4.897e+85 Derivative of order w.r.t (n-1)th term = 2.503e+86 Derivative of radius w.r.t (n-2)th term = -9.417e+82 Derivative of order w.r.t (n-2)th term = -4.739e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.052e+31 Guess error in order = -6.079e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.300000000000003 y[1] (analytic) = 0.0368831674012399 y[1] (numeric) = 0.03688316740124002 absolute error = 1.249000902703301e-16 relative error = 3.386371048657046e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.2 Radius of convergence (three term test) for eq 1 = 3.505e+15 Order of pole (three term test) = 3.505e+15 Derivative of radius w.r.t nth term = 3.625e+87 Derivative of order w.r.t nth term = -3.625e+87 Derivative of radius w.r.t (n-1)th term = 2.685e+85 Derivative of order w.r.t (n-1)th term = 1.373e+86 Derivative of radius w.r.t (n-2)th term = -5.164e+82 Derivative of order w.r.t (n-2)th term = -2.128e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.456e+31 Guess error in order = -3.684e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.200000000000003 y[1] (analytic) = 0.0407622039783661 y[1] (numeric) = 0.04076220397836623 absolute error = 1.318389841742373e-16 relative error = 3.234343860410708e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.2 Radius of convergence (three term test) for eq 1 = 1.343e+16 Order of pole (three term test) = 1.343e+16 Derivative of radius w.r.t nth term = 4.82e+88 Derivative of order w.r.t nth term = -4.82e+88 Derivative of radius w.r.t (n-1)th term = 3.57e+86 Derivative of order w.r.t (n-1)th term = 1.825e+87 Derivative of radius w.r.t (n-2)th term = -6.866e+83 Derivative of order w.r.t (n-2)th term = -2.316e+193 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.609e+32 Guess error in order = -5.413e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.100000000000003 y[1] (analytic) = 0.04504920239355768 y[1] (numeric) = 0.04504920239355782 absolute error = 1.387778780781446e-16 relative error = 3.080584576520509e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.3 Radius of convergence (three term test) for eq 1 = 8.56e+15 Order of pole (three term test) = 8.56e+15 Derivative of radius w.r.t nth term = 1.774e+88 Derivative of order w.r.t nth term = -1.774e+88 Derivative of radius w.r.t (n-1)th term = 1.314e+86 Derivative of order w.r.t (n-1)th term = 6.715e+86 Derivative of radius w.r.t (n-2)th term = -2.527e+83 Derivative of order w.r.t (n-2)th term = -6.978e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.468e+32 Guess error in order = -2.201e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -3.000000000000003 y[1] (analytic) = 0.04978706836786381 y[1] (numeric) = 0.04978706836786396 absolute error = 1.457167719820518e-16 relative error = 2.926799603973227e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.3 Radius of convergence (three term test) for eq 1 = 4.124e+16 Order of pole (three term test) = 4.124e+16 Derivative of radius w.r.t nth term = 3.72e+89 Derivative of order w.r.t nth term = -3.72e+89 Derivative of radius w.r.t (n-1)th term = 2.756e+87 Derivative of order w.r.t (n-1)th term = 1.408e+88 Derivative of radius w.r.t (n-2)th term = -5.299e+84 Derivative of order w.r.t (n-2)th term = -1.198e+194 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.402e+33 Guess error in order = -5.103e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.900000000000003 y[1] (analytic) = 0.05502322005640709 y[1] (numeric) = 0.05502322005640724 absolute error = 1.595945597898663e-16 relative error = 2.900494729793309e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.3 Radius of convergence (three term test) for eq 1 = 1.481e+16 Order of pole (three term test) = 1.481e+16 Derivative of radius w.r.t nth term = 4.348e+88 Derivative of order w.r.t nth term = -4.348e+88 Derivative of radius w.r.t (n-1)th term = 3.221e+86 Derivative of order w.r.t (n-1)th term = 1.646e+87 Derivative of radius w.r.t (n-2)th term = -6.194e+83 Derivative of order w.r.t (n-2)th term = -1.147e+193 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.394e+32 Guess error in order = -6.591e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.800000000000002 y[1] (analytic) = 0.06081006262521781 y[1] (numeric) = 0.06081006262521798 absolute error = 1.665334536937735e-16 relative error = 2.738583821564959e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.4 Radius of convergence (three term test) for eq 1 = 5.099e+15 Order of pole (three term test) = 5.099e+15 Derivative of radius w.r.t nth term = 4.655e+87 Derivative of order w.r.t nth term = -4.655e+87 Derivative of radius w.r.t (n-1)th term = 3.448e+85 Derivative of order w.r.t (n-1)th term = 1.762e+86 Derivative of radius w.r.t (n-2)th term = -6.631e+82 Derivative of order w.r.t (n-2)th term = -1.005e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 5.199e+31 Guess error in order = -7.799e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.700000000000002 y[1] (analytic) = 0.0672055127397496 y[1] (numeric) = 0.06720551273974978 absolute error = 1.804112415015879e-16 relative error = 2.684470873694879e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.4 Radius of convergence (three term test) for eq 1 = 5.123e+15 Order of pole (three term test) = 5.123e+15 Derivative of radius w.r.t nth term = 4.245e+87 Derivative of order w.r.t nth term = -4.245e+87 Derivative of radius w.r.t (n-1)th term = 3.144e+85 Derivative of order w.r.t (n-1)th term = 1.607e+86 Derivative of radius w.r.t (n-2)th term = -6.047e+82 Derivative of order w.r.t (n-2)th term = -7.504e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 5.24e+31 Guess error in order = -7.86e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.600000000000002 y[1] (analytic) = 0.07427357821433371 y[1] (numeric) = 0.0742735782143339 absolute error = 1.942890293094024e-16 relative error = 2.615856593696565e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.4 Radius of convergence (three term test) for eq 1 = 1.022e+16 Order of pole (three term test) = 1.022e+16 Derivative of radius w.r.t nth term = 1.53e+88 Derivative of order w.r.t nth term = -1.53e+88 Derivative of radius w.r.t (n-1)th term = 1.133e+86 Derivative of order w.r.t (n-1)th term = 5.793e+86 Derivative of radius w.r.t (n-2)th term = -2.18e+83 Derivative of order w.r.t (n-2)th term = -2.215e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.087e+32 Guess error in order = -3.131e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.500000000000002 y[1] (analytic) = 0.08208499862389862 y[1] (numeric) = 0.08208499862389883 absolute error = 2.081668171172169e-16 relative error = 2.535990992349364e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.5 Radius of convergence (three term test) for eq 1 = 6.198e+15 Order of pole (three term test) = 6.198e+15 Derivative of radius w.r.t nth term = 5.096e+87 Derivative of order w.r.t nth term = -5.096e+87 Derivative of radius w.r.t (n-1)th term = 3.775e+85 Derivative of order w.r.t (n-1)th term = 1.93e+86 Derivative of radius w.r.t (n-2)th term = -7.26e+82 Derivative of order w.r.t (n-2)th term = -6.039e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.684e+31 Guess error in order = -1.153e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.400000000000002 y[1] (analytic) = 0.0907179532894123 y[1] (numeric) = 0.09071795328941254 absolute error = 2.359223927328458e-16 relative error = 2.600614147237163e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.5 Radius of convergence (three term test) for eq 1 = 1.235e+16 Order of pole (three term test) = 1.235e+16 Derivative of radius w.r.t nth term = 1.826e+88 Derivative of order w.r.t nth term = -1.826e+88 Derivative of radius w.r.t (n-1)th term = 1.353e+86 Derivative of order w.r.t (n-1)th term = 6.914e+86 Derivative of radius w.r.t (n-2)th term = -2.602e+83 Derivative of order w.r.t (n-2)th term = -1.772e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.043e+32 Guess error in order = -4.565e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.300000000000002 y[1] (analytic) = 0.1002588437228035 y[1] (numeric) = 0.1002588437228038 absolute error = 2.498001805406602e-16 relative error = 2.491552577958208e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.5 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.200000000000002 y[1] (analytic) = 0.1108031583623337 y[1] (numeric) = 0.1108031583623339 absolute error = 2.636779683484747e-16 relative error = 2.379697223848352e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.6 Radius of convergence (three term test) for eq 1 = 8.326e+15 Order of pole (three term test) = 8.326e+15 Derivative of radius w.r.t nth term = 6.819e+87 Derivative of order w.r.t nth term = -6.819e+87 Derivative of radius w.r.t (n-1)th term = 5.051e+85 Derivative of order w.r.t (n-1)th term = 2.582e+86 Derivative of radius w.r.t (n-2)th term = -9.713e+82 Derivative of order w.r.t (n-2)th term = -4.434e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.388e+32 Guess error in order = -2.082e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.100000000000002 y[1] (analytic) = 0.1224564282529817 y[1] (numeric) = 0.122456428252982 absolute error = 2.775557561562891e-16 relative error = 2.266567464983456e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.6 Radius of convergence (three term test) for eq 1 = 8.425e+15 Order of pole (three term test) = 8.425e+15 Derivative of radius w.r.t nth term = 6.321e+87 Derivative of order w.r.t nth term = -6.321e+87 Derivative of radius w.r.t (n-1)th term = 4.683e+85 Derivative of order w.r.t (n-1)th term = 2.393e+86 Derivative of radius w.r.t (n-2)th term = -9.005e+82 Derivative of order w.r.t (n-2)th term = -3.366e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.422e+32 Guess error in order = -2.133e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -2.000000000000002 y[1] (analytic) = 0.1353352832366125 y[1] (numeric) = 0.1353352832366128 absolute error = 3.05311331771918e-16 relative error = 2.255962558101934e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.6 Radius of convergence (three term test) for eq 1 = 5.638e+15 Order of pole (three term test) = 5.638e+15 Derivative of radius w.r.t nth term = 2.557e+87 Derivative of order w.r.t nth term = -2.557e+87 Derivative of radius w.r.t (n-1)th term = 1.894e+85 Derivative of order w.r.t (n-1)th term = 9.682e+85 Derivative of radius w.r.t (n-2)th term = -3.643e+82 Derivative of order w.r.t (n-2)th term = -1.115e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.357e+31 Guess error in order = -9.535e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.900000000000002 y[1] (analytic) = 0.1495686192226348 y[1] (numeric) = 0.1495686192226351 absolute error = 3.05311331771918e-16 relative error = 2.041279336258752e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.6 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.800000000000002 y[1] (analytic) = 0.1652988882215863 y[1] (numeric) = 0.1652988882215866 absolute error = 3.33066907387547e-16 relative error = 2.014937371756938e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.7 Radius of convergence (three term test) for eq 1 = 1.136e+16 Order of pole (three term test) = 1.136e+16 Derivative of radius w.r.t nth term = 8.5e+87 Derivative of order w.r.t nth term = -8.5e+87 Derivative of radius w.r.t (n-1)th term = 6.296e+85 Derivative of order w.r.t (n-1)th term = 3.218e+86 Derivative of radius w.r.t (n-2)th term = -1.211e+83 Derivative of order w.r.t (n-2)th term = -2.484e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.581e+32 Guess error in order = -3.871e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.700000000000002 y[1] (analytic) = 0.1826835240527344 y[1] (numeric) = 0.1826835240527347 absolute error = 3.608224830031759e-16 relative error = 1.975123289711769e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.7 Radius of convergence (three term test) for eq 1 = 6.305e+15 Order of pole (three term test) = 6.305e+15 Derivative of radius w.r.t nth term = 2.369e+87 Derivative of order w.r.t nth term = -2.369e+87 Derivative of radius w.r.t (n-1)th term = 1.755e+85 Derivative of order w.r.t (n-1)th term = 8.971e+85 Derivative of radius w.r.t (n-2)th term = -3.375e+82 Derivative of order w.r.t (n-2)th term = -5.669e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.951e+31 Guess error in order = -1.193e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.600000000000001 y[1] (analytic) = 0.2018965179946551 y[1] (numeric) = 0.2018965179946555 absolute error = 3.885780586188048e-16 relative error = 1.924639723747448e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.7 Radius of convergence (three term test) for eq 1 = 9.521e+15 Order of pole (three term test) = 9.521e+15 Derivative of radius w.r.t nth term = 4.889e+87 Derivative of order w.r.t nth term = -4.889e+87 Derivative of radius w.r.t (n-1)th term = 3.621e+85 Derivative of order w.r.t (n-1)th term = 1.851e+86 Derivative of radius w.r.t (n-2)th term = -6.964e+82 Derivative of order w.r.t (n-2)th term = -9.576e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.813e+32 Guess error in order = -2.719e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.500000000000001 y[1] (analytic) = 0.2231301601484295 y[1] (numeric) = 0.22313016014843 absolute error = 4.163336342344337e-16 relative error = 1.865877898162589e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.8 Radius of convergence (three term test) for eq 1 = 4.03e+16 Order of pole (three term test) = 4.03e+16 Derivative of radius w.r.t nth term = 7.964e+88 Derivative of order w.r.t nth term = -7.964e+88 Derivative of radius w.r.t (n-1)th term = 5.9e+86 Derivative of order w.r.t (n-1)th term = 3.015e+87 Derivative of radius w.r.t (n-2)th term = -1.135e+84 Derivative of order w.r.t (n-2)th term = -1.277e+192 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.264e+33 Guess error in order = -4.896e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.400000000000001 y[1] (analytic) = 0.2465969639416062 y[1] (numeric) = 0.2465969639416066 absolute error = 4.718447854656915e-16 relative error = 1.913424958376307e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.8 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.300000000000001 y[1] (analytic) = 0.2725317930340123 y[1] (numeric) = 0.2725317930340128 absolute error = 4.440892098500626e-16 relative error = 1.6294950578285e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.8 Radius of convergence (three term test) for eq 1 = 4.64e+15 Order of pole (three term test) = 4.64e+15 Derivative of radius w.r.t nth term = 8.597e+86 Derivative of order w.r.t nth term = -8.597e+86 Derivative of radius w.r.t (n-1)th term = 6.368e+84 Derivative of order w.r.t (n-1)th term = 3.255e+85 Derivative of radius w.r.t (n-2)th term = -1.225e+82 Derivative of order w.r.t (n-2)th term = -9.241e+189 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.303e+31 Guess error in order = -6.455e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.200000000000001 y[1] (analytic) = 0.3011942119122017 y[1] (numeric) = 0.3011942119122022 absolute error = 4.996003610813204e-16 relative error = 1.658731613431383e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.9 Radius of convergence (three term test) for eq 1 = 3.962e+16 Order of pole (three term test) = 3.962e+16 Derivative of radius w.r.t nth term = 5.645e+88 Derivative of order w.r.t nth term = -5.645e+88 Derivative of radius w.r.t (n-1)th term = 4.181e+86 Derivative of order w.r.t (n-1)th term = 2.137e+87 Derivative of radius w.r.t (n-2)th term = -8.041e+83 Derivative of order w.r.t (n-2)th term = -4.968e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.123e+33 Guess error in order = -4.684e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.100000000000001 y[1] (analytic) = 0.3328710836980792 y[1] (numeric) = 0.3328710836980797 absolute error = 4.996003610813204e-16 relative error = 1.500882430311874e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.9 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.000000000000001 y[1] (analytic) = 0.367879441171442 y[1] (numeric) = 0.3678794411714425 absolute error = 4.996003610813204e-16 relative error = 1.358054583018932e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 126.9 Radius of convergence (three term test) for eq 1 = 4.839e+15 Order of pole (three term test) = 4.839e+15 Derivative of radius w.r.t nth term = 6.931e+86 Derivative of order w.r.t nth term = -6.931e+86 Derivative of radius w.r.t (n-1)th term = 5.134e+84 Derivative of order w.r.t (n-1)th term = 2.624e+85 Derivative of radius w.r.t (n-2)th term = -9.873e+81 Derivative of order w.r.t (n-2)th term = -4.089e+189 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.683e+31 Guess error in order = -7.025e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.9000000000000009 y[1] (analytic) = 0.4065696597405987 y[1] (numeric) = 0.4065696597405993 absolute error = 6.106226635438361e-16 relative error = 1.501889402995364e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127 Radius of convergence (three term test) for eq 1 = 3.867e+16 Order of pole (three term test) = 3.867e+16 Derivative of radius w.r.t nth term = 4.006e+88 Derivative of order w.r.t nth term = -4.006e+88 Derivative of radius w.r.t (n-1)th term = 2.967e+86 Derivative of order w.r.t (n-1)th term = 1.517e+87 Derivative of radius w.r.t (n-2)th term = -5.706e+83 Derivative of order w.r.t (n-2)th term = -1.935e+191 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.991e+33 Guess error in order = -4.487e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.8000000000000009 y[1] (analytic) = 0.4493289641172212 y[1] (numeric) = 0.4493289641172218 absolute error = 6.661338147750939e-16 relative error = 1.482508068634793e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127 Radius of convergence (three term test) for eq 1 = 2.372e+16 Order of pole (three term test) = 2.372e+16 Derivative of radius w.r.t nth term = 1.36e+88 Derivative of order w.r.t nth term = -1.36e+88 Derivative of radius w.r.t (n-1)th term = 1.008e+86 Derivative of order w.r.t (n-1)th term = 5.15e+86 Derivative of radius w.r.t (n-2)th term = -1.938e+83 Derivative of order w.r.t (n-2)th term = -5.379e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.123e+33 Guess error in order = -1.684e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.700000000000001 y[1] (analytic) = 0.496585303791409 y[1] (numeric) = 0.4965853037914098 absolute error = 7.771561172376096e-16 relative error = 1.565000235214481e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.600000000000001 y[1] (analytic) = 0.5488116360940259 y[1] (numeric) = 0.5488116360940267 absolute error = 7.771561172376096e-16 relative error = 1.41607077205714e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.425e+07 Order of pole (six term test) = -2.151e+14 TOP MAIN SOLVE Loop x[1] = -0.500000000000001 y[1] (analytic) = 0.6065306597126329 y[1] (numeric) = 0.6065306597126338 absolute error = 8.881784197001252e-16 relative error = 1.464358652736424e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.1 Radius of convergence (three term test) for eq 1 = 3.392e+16 Order of pole (three term test) = 3.392e+16 Derivative of radius w.r.t nth term = 2.065e+88 Derivative of order w.r.t nth term = -2.065e+88 Derivative of radius w.r.t (n-1)th term = 1.53e+86 Derivative of order w.r.t (n-1)th term = 7.818e+86 Derivative of radius w.r.t (n-2)th term = -2.942e+83 Derivative of order w.r.t (n-2)th term = -4.482e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.301e+33 Guess error in order = -3.451e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.400000000000001 y[1] (analytic) = 0.6703200460356387 y[1] (numeric) = 0.6703200460356397 absolute error = 9.992007221626409e-16 relative error = 1.490632315223222e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.1 Radius of convergence (three term test) for eq 1 = 2.543e+16 Order of pole (three term test) = 2.543e+16 Derivative of radius w.r.t nth term = 1.051e+88 Derivative of order w.r.t nth term = -1.051e+88 Derivative of radius w.r.t (n-1)th term = 7.782e+85 Derivative of order w.r.t (n-1)th term = 3.977e+86 Derivative of radius w.r.t (n-2)th term = -1.496e+83 Derivative of order w.r.t (n-2)th term = -1.867e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.293e+33 Guess error in order = -1.94e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.300000000000001 y[1] (analytic) = 0.7408182206817171 y[1] (numeric) = 0.7408182206817182 absolute error = 1.110223024625157e-15 relative error = 1.498644328163939e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.2 Radius of convergence (three term test) for eq 1 = 6.94e+15 Order of pole (three term test) = 6.94e+15 Derivative of radius w.r.t nth term = 7.088e+86 Derivative of order w.r.t nth term = -7.088e+86 Derivative of radius w.r.t (n-1)th term = 5.251e+84 Derivative of order w.r.t (n-1)th term = 2.684e+85 Derivative of radius w.r.t (n-2)th term = -1.01e+82 Derivative of order w.r.t (n-2)th term = -1.031e+189 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 9.645e+31 Guess error in order = -1.447e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.200000000000001 y[1] (analytic) = 0.818730753077981 y[1] (numeric) = 0.8187307530779823 absolute error = 1.221245327087672e-15 relative error = 1.491632410895103e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.2 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -0.100000000000001 y[1] (analytic) = 0.9048374180359586 y[1] (numeric) = 0.9048374180359601 absolute error = 1.443289932012704e-15 relative error = 1.59508205921182e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.2 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = -1.02695629777827e-15 y[1] (analytic) = 0.999999999999999 y[1] (numeric) = 1 absolute error = 1.443289932012704e-15 relative error = 1.443289932012705e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.2 Radius of convergence (three term test) for eq 1 = 8.083e+15 Order of pole (three term test) = 8.083e+15 Derivative of radius w.r.t nth term = 7.114e+86 Derivative of order w.r.t nth term = -7.114e+86 Derivative of radius w.r.t (n-1)th term = 5.269e+84 Derivative of order w.r.t (n-1)th term = 2.693e+85 Derivative of radius w.r.t (n-2)th term = -1.013e+82 Derivative of order w.r.t (n-2)th term = -5.68e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.307e+32 Guess error in order = -1.96e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.09999999999999898 y[1] (analytic) = 1.105170918075647 y[1] (numeric) = 1.105170918075648 absolute error = 1.554312234475219e-15 relative error = 1.406399869064262e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.3 Radius of convergence (three term test) for eq 1 = 5.373e+15 Order of pole (three term test) = 5.373e+15 Derivative of radius w.r.t nth term = 2.844e+86 Derivative of order w.r.t nth term = -2.844e+86 Derivative of radius w.r.t (n-1)th term = 2.107e+84 Derivative of order w.r.t (n-1)th term = 1.077e+85 Derivative of radius w.r.t (n-2)th term = -4.052e+81 Derivative of order w.r.t (n-2)th term = -1.859e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 5.774e+31 Guess error in order = -8.66e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.199999999999999 y[1] (analytic) = 1.221402758160169 y[1] (numeric) = 1.221402758160171 absolute error = 1.998401444325282e-15 relative error = 1.636152719464566e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.3 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.299999999999999 y[1] (analytic) = 1.349858807576002 y[1] (numeric) = 1.349858807576004 absolute error = 1.998401444325282e-15 relative error = 1.480452202192832e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.3 Radius of convergence (three term test) for eq 1 = 1.099e+17 Order of pole (three term test) = 1.099e+17 Derivative of radius w.r.t nth term = 9.745e+88 Derivative of order w.r.t nth term = -9.745e+88 Derivative of radius w.r.t (n-1)th term = 7.219e+86 Derivative of order w.r.t (n-1)th term = 3.69e+87 Derivative of radius w.r.t (n-2)th term = -1.388e+84 Derivative of order w.r.t (n-2)th term = -4.27e+190 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.416e+34 Guess error in order = -3.624e+34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.399999999999999 y[1] (analytic) = 1.491824697641269 y[1] (numeric) = 1.491824697641271 absolute error = 2.442490654175344e-15 relative error = 1.637250447748437e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.4 Radius of convergence (three term test) for eq 1 = 7.142e+15 Order of pole (three term test) = 7.142e+15 Derivative of radius w.r.t nth term = 3.723e+86 Derivative of order w.r.t nth term = -3.723e+86 Derivative of radius w.r.t (n-1)th term = 2.758e+84 Derivative of order w.r.t (n-1)th term = 1.41e+85 Derivative of radius w.r.t (n-2)th term = -5.304e+81 Derivative of order w.r.t (n-2)th term = -1.336e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.02e+32 Guess error in order = -1.53e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.499999999999999 y[1] (analytic) = 1.648721270700126 y[1] (numeric) = 1.648721270700129 absolute error = 2.664535259100376e-15 relative error = 1.616122328529725e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.4 Radius of convergence (three term test) for eq 1 = 1.301e+16 Order of pole (three term test) = 1.301e+16 Derivative of radius w.r.t nth term = 1.115e+87 Derivative of order w.r.t nth term = -1.115e+87 Derivative of radius w.r.t (n-1)th term = 8.26e+84 Derivative of order w.r.t (n-1)th term = 4.222e+85 Derivative of radius w.r.t (n-2)th term = -1.588e+82 Derivative of order w.r.t (n-2)th term = -3.275e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.377e+32 Guess error in order = -5.065e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.599999999999999 y[1] (analytic) = 1.822118800390507 y[1] (numeric) = 1.82211880039051 absolute error = 2.886579864025407e-15 relative error = 1.584188617891858e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.4 Radius of convergence (three term test) for eq 1 = 6.186e+15 Order of pole (three term test) = 6.186e+15 Derivative of radius w.r.t nth term = 2.283e+86 Derivative of order w.r.t nth term = -2.283e+86 Derivative of radius w.r.t (n-1)th term = 1.691e+84 Derivative of order w.r.t (n-1)th term = 8.644e+84 Derivative of radius w.r.t (n-2)th term = -3.253e+81 Derivative of order w.r.t (n-2)th term = -5.491e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.642e+31 Guess error in order = -1.146e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.699999999999999 y[1] (analytic) = 2.013752707470474 y[1] (numeric) = 2.013752707470478 absolute error = 3.108624468950438e-15 relative error = 1.543697226287164e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.5 Radius of convergence (three term test) for eq 1 = 2.364e+16 Order of pole (three term test) = 2.364e+16 Derivative of radius w.r.t nth term = 3.021e+87 Derivative of order w.r.t nth term = -3.021e+87 Derivative of radius w.r.t (n-1)th term = 2.238e+85 Derivative of order w.r.t (n-1)th term = 1.144e+86 Derivative of radius w.r.t (n-2)th term = -4.303e+82 Derivative of order w.r.t (n-2)th term = -5.948e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.117e+33 Guess error in order = -1.676e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.7999999999999989 y[1] (analytic) = 2.225540928492465 y[1] (numeric) = 2.225540928492469 absolute error = 3.552713678800501e-15 relative error = 1.596337157100514e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.5 Radius of convergence (three term test) for eq 1 = 3.83e+15 Order of pole (three term test) = 3.83e+15 Derivative of radius w.r.t nth term = 7.178e+85 Derivative of order w.r.t nth term = -7.178e+85 Derivative of radius w.r.t (n-1)th term = 5.317e+83 Derivative of order w.r.t (n-1)th term = 2.718e+84 Derivative of radius w.r.t (n-2)th term = -1.023e+81 Derivative of order w.r.t (n-2)th term = -1.157e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.934e+31 Guess error in order = -4.402e+31 Radius of convergence (six term test) for eq 1 = 4.789e+07 Order of pole (six term test) = -1.971e+14 TOP MAIN SOLVE Loop x[1] = 0.8999999999999989 y[1] (analytic) = 2.459603111156947 y[1] (numeric) = 2.459603111156951 absolute error = 3.552713678800501e-15 relative error = 1.444425591545693e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.5 Radius of convergence (three term test) for eq 1 = 2.051e+16 Order of pole (three term test) = 2.051e+16 Derivative of radius w.r.t nth term = 1.866e+87 Derivative of order w.r.t nth term = -1.866e+87 Derivative of radius w.r.t (n-1)th term = 1.382e+85 Derivative of order w.r.t (n-1)th term = 7.065e+85 Derivative of radius w.r.t (n-2)th term = -2.658e+82 Derivative of order w.r.t (n-2)th term = -2.463e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 8.431e+32 Guess error in order = -1.265e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 0.9999999999999989 y[1] (analytic) = 2.718281828459042 y[1] (numeric) = 2.718281828459046 absolute error = 3.996802888650564e-15 relative error = 1.470341613149177e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.6 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.099999999999999 y[1] (analytic) = 3.00416602394643 y[1] (numeric) = 3.004166023946434 absolute error = 4.440892098500626e-15 relative error = 1.478244565414144e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.6 Radius of convergence (three term test) for eq 1 = 6.032e+15 Order of pole (three term test) = 6.032e+15 Derivative of radius w.r.t nth term = 1.319e+86 Derivative of order w.r.t nth term = -1.319e+86 Derivative of radius w.r.t (n-1)th term = 9.77e+83 Derivative of order w.r.t (n-1)th term = 4.993e+84 Derivative of radius w.r.t (n-2)th term = -1.879e+81 Derivative of order w.r.t (n-2)th term = -1.167e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.277e+31 Guess error in order = -1.092e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.199999999999999 y[1] (analytic) = 3.320116922736545 y[1] (numeric) = 3.320116922736549 absolute error = 4.440892098500626e-15 relative error = 1.337570995795023e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.6 Radius of convergence (three term test) for eq 1 = 6.897e+15 Order of pole (three term test) = 6.897e+15 Derivative of radius w.r.t nth term = 1.56e+86 Derivative of order w.r.t nth term = -1.56e+86 Derivative of radius w.r.t (n-1)th term = 1.156e+84 Derivative of order w.r.t (n-1)th term = 5.906e+84 Derivative of radius w.r.t (n-2)th term = -2.222e+81 Derivative of order w.r.t (n-2)th term = -1.13e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 9.513e+31 Guess error in order = -1.427e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.299999999999999 y[1] (analytic) = 3.669296667619241 y[1] (numeric) = 3.669296667619246 absolute error = 4.440892098500626e-15 relative error = 1.210284286274956e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.7 Radius of convergence (three term test) for eq 1 = 5.985e+15 Order of pole (three term test) = 5.985e+15 Derivative of radius w.r.t nth term = 1.062e+86 Derivative of order w.r.t nth term = -1.062e+86 Derivative of radius w.r.t (n-1)th term = 7.869e+83 Derivative of order w.r.t (n-1)th term = 4.022e+84 Derivative of radius w.r.t (n-2)th term = -1.513e+81 Derivative of order w.r.t (n-2)th term = -6.3e+186 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.159e+31 Guess error in order = -1.074e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.399999999999999 y[1] (analytic) = 4.055199966844672 y[1] (numeric) = 4.055199966844676 absolute error = 4.440892098500626e-15 relative error = 1.095110508682525e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.7 Radius of convergence (three term test) for eq 1 = 8.989e+15 Order of pole (three term test) = 8.989e+15 Derivative of radius w.r.t nth term = 2.17e+86 Derivative of order w.r.t nth term = -2.17e+86 Derivative of radius w.r.t (n-1)th term = 1.607e+84 Derivative of order w.r.t (n-1)th term = 8.214e+84 Derivative of radius w.r.t (n-2)th term = -3.091e+81 Derivative of order w.r.t (n-2)th term = -1.053e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.616e+32 Guess error in order = -2.424e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.499999999999999 y[1] (analytic) = 4.481689070338062 y[1] (numeric) = 4.481689070338067 absolute error = 5.329070518200751e-15 relative error = 1.18907635816841e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.7 Radius of convergence (three term test) for eq 1 = 3.801e+16 Order of pole (three term test) = 3.801e+16 Derivative of radius w.r.t nth term = 3.51e+87 Derivative of order w.r.t nth term = -3.51e+87 Derivative of radius w.r.t (n-1)th term = 2.6e+85 Derivative of order w.r.t (n-1)th term = 1.329e+86 Derivative of radius w.r.t (n-2)th term = -5.001e+82 Derivative of order w.r.t (n-2)th term = -1.395e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.89e+33 Guess error in order = -4.335e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.599999999999999 y[1] (analytic) = 4.953032424395112 y[1] (numeric) = 4.953032424395118 absolute error = 5.329070518200751e-15 relative error = 1.075920781772706e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.7 Radius of convergence (three term test) for eq 1 = 1.281e+17 Order of pole (three term test) = 1.281e+17 Derivative of radius w.r.t nth term = 3.665e+88 Derivative of order w.r.t nth term = -3.665e+88 Derivative of radius w.r.t (n-1)th term = 2.714e+86 Derivative of order w.r.t (n-1)th term = 1.387e+87 Derivative of radius w.r.t (n-2)th term = -5.22e+83 Derivative of order w.r.t (n-2)th term = -1.193e+189 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.334e+34 Guess error in order = -5.001e+34 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.7 y[1] (analytic) = 5.473947391727197 y[1] (numeric) = 5.473947391727203 absolute error = 5.329070518200751e-15 relative error = 9.735333821904465e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.8 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.8 y[1] (analytic) = 6.049647464412944 y[1] (numeric) = 6.049647464412949 absolute error = 5.329070518200751e-15 relative error = 8.808894319130186e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.8 Radius of convergence (three term test) for eq 1 = 5.388e+15 Order of pole (three term test) = 5.388e+15 Derivative of radius w.r.t nth term = 5.226e+85 Derivative of order w.r.t nth term = -5.226e+85 Derivative of radius w.r.t (n-1)th term = 3.871e+83 Derivative of order w.r.t (n-1)th term = 1.979e+84 Derivative of radius w.r.t (n-2)th term = -7.444e+80 Derivative of order w.r.t (n-2)th term = -1.14e+186 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 5.807e+31 Guess error in order = -8.71e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 1.9 y[1] (analytic) = 6.685894442279268 y[1] (numeric) = 6.685894442279273 absolute error = 5.329070518200751e-15 relative error = 7.970617191473388e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.8 Radius of convergence (three term test) for eq 1 = 1.056e+16 Order of pole (three term test) = 1.056e+16 Derivative of radius w.r.t nth term = 1.819e+86 Derivative of order w.r.t nth term = -1.819e+86 Derivative of radius w.r.t (n-1)th term = 1.347e+84 Derivative of order w.r.t (n-1)th term = 6.887e+84 Derivative of radius w.r.t (n-2)th term = -2.591e+81 Derivative of order w.r.t (n-2)th term = -3.249e+186 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.234e+32 Guess error in order = -3.351e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 7.389056098930649 y[1] (numeric) = 7.389056098930654 absolute error = 5.329070518200751e-15 relative error = 7.212112679685812e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.9 Radius of convergence (three term test) for eq 1 = 5.791e+15 Order of pole (three term test) = 5.791e+15 Derivative of radius w.r.t nth term = 4.942e+85 Derivative of order w.r.t nth term = -4.942e+85 Derivative of radius w.r.t (n-1)th term = 3.661e+83 Derivative of order w.r.t (n-1)th term = 1.871e+84 Derivative of radius w.r.t (n-2)th term = -7.04e+80 Derivative of order w.r.t (n-2)th term = -7.227e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.707e+31 Guess error in order = -1.006e+32 Radius of convergence (six term test) for eq 1 = 4.952e+07 Order of pole (six term test) = -2.33e+14 TOP MAIN SOLVE Loop x[1] = 2.1 y[1] (analytic) = 8.166169912567646 y[1] (numeric) = 8.166169912567653 absolute error = 7.105427357601002e-15 relative error = 8.701052554228423e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.9 Radius of convergence (three term test) for eq 1 = 2.725e+16 Order of pole (three term test) = 2.725e+16 Derivative of radius w.r.t nth term = 9.95e+86 Derivative of order w.r.t nth term = -9.95e+86 Derivative of radius w.r.t (n-1)th term = 7.37e+84 Derivative of order w.r.t (n-1)th term = 3.767e+85 Derivative of radius w.r.t (n-2)th term = -1.417e+82 Derivative of order w.r.t (n-2)th term = -1.191e+187 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.492e+33 Guess error in order = -2.239e+33 Radius of convergence (six term test) for eq 1 = 1.91e+08 Order of pole (six term test) = -7.13e+14 TOP MAIN SOLVE Loop x[1] = 2.2 y[1] (analytic) = 9.025013499434118 y[1] (numeric) = 9.025013499434124 absolute error = 5.329070518200751e-15 relative error = 5.904778445522427e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 127.9 Radius of convergence (three term test) for eq 1 = 9.915e+15 Order of pole (three term test) = 9.915e+15 Derivative of radius w.r.t nth term = 1.188e+86 Derivative of order w.r.t nth term = -1.188e+86 Derivative of radius w.r.t (n-1)th term = 8.799e+83 Derivative of order w.r.t (n-1)th term = 4.497e+84 Derivative of radius w.r.t (n-2)th term = -1.692e+81 Derivative of order w.r.t (n-2)th term = -1.164e+186 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.969e+32 Guess error in order = -2.954e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.3 y[1] (analytic) = 9.974182454814718 y[1] (numeric) = 9.974182454814724 absolute error = 5.329070518200751e-15 relative error = 5.3428644827209e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.4 y[1] (analytic) = 11.0231763806416 y[1] (numeric) = 11.0231763806416 absolute error = 3.552713678800501e-15 relative error = 3.222949135640807e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128 Radius of convergence (three term test) for eq 1 = 7.96e+15 Order of pole (three term test) = 7.96e+15 Derivative of radius w.r.t nth term = 6.269e+85 Derivative of order w.r.t nth term = -6.269e+85 Derivative of radius w.r.t (n-1)th term = 4.644e+83 Derivative of order w.r.t (n-1)th term = 2.374e+84 Derivative of radius w.r.t (n-2)th term = -8.931e+80 Derivative of order w.r.t (n-2)th term = -4.12e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.269e+32 Guess error in order = -1.904e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.5 y[1] (analytic) = 12.18249396070347 y[1] (numeric) = 12.18249396070348 absolute error = 3.552713678800501e-15 relative error = 2.916244974354456e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128 Radius of convergence (three term test) for eq 1 = 2.449e+17 Order of pole (three term test) = 2.449e+17 Derivative of radius w.r.t nth term = 5.361e+88 Derivative of order w.r.t nth term = -5.361e+88 Derivative of radius w.r.t (n-1)th term = 3.971e+86 Derivative of order w.r.t (n-1)th term = 2.03e+87 Derivative of radius w.r.t (n-2)th term = -7.637e+83 Derivative of order w.r.t (n-2)th term = -2.884e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.2e+35 Guess error in order = -1.799e+35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.6 y[1] (analytic) = 13.46373803500169 y[1] (numeric) = 13.46373803500169 absolute error = 1.77635683940025e-15 relative error = 1.319363786477614e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.1 Radius of convergence (three term test) for eq 1 = 1.177e+16 Order of pole (three term test) = 1.177e+16 Derivative of radius w.r.t nth term = 1.119e+86 Derivative of order w.r.t nth term = -1.119e+86 Derivative of radius w.r.t (n-1)th term = 8.287e+83 Derivative of order w.r.t (n-1)th term = 4.236e+84 Derivative of radius w.r.t (n-2)th term = -1.594e+81 Derivative of order w.r.t (n-2)th term = -4.928e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.767e+32 Guess error in order = -4.15e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.7 y[1] (analytic) = 14.87973172487284 y[1] (numeric) = 14.87973172487284 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.1 Radius of convergence (three term test) for eq 1 = 7.965e+15 Order of pole (three term test) = 7.965e+15 Derivative of radius w.r.t nth term = 4.646e+85 Derivative of order w.r.t nth term = -4.646e+85 Derivative of radius w.r.t (n-1)th term = 3.442e+83 Derivative of order w.r.t (n-1)th term = 1.759e+84 Derivative of radius w.r.t (n-2)th term = -6.619e+80 Derivative of order w.r.t (n-2)th term = -1.676e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.27e+32 Guess error in order = -1.905e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.8 y[1] (analytic) = 16.44464677109706 y[1] (numeric) = 16.44464677109705 absolute error = 3.552713678800501e-15 relative error = 2.160407412973269e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.1 Radius of convergence (three term test) for eq 1 = 6.199e+15 Order of pole (three term test) = 6.199e+15 Derivative of radius w.r.t nth term = 2.544e+85 Derivative of order w.r.t nth term = -2.544e+85 Derivative of radius w.r.t (n-1)th term = 1.885e+83 Derivative of order w.r.t (n-1)th term = 9.633e+83 Derivative of radius w.r.t (n-2)th term = -3.624e+80 Derivative of order w.r.t (n-2)th term = -7.512e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 7.685e+31 Guess error in order = -1.153e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 2.9 y[1] (analytic) = 18.17414536944307 y[1] (numeric) = 18.17414536944306 absolute error = 3.552713678800501e-15 relative error = 1.95481746546048e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.2 Radius of convergence (three term test) for eq 1 = 1.74e+16 Order of pole (three term test) = 1.74e+16 Derivative of radius w.r.t nth term = 1.815e+86 Derivative of order w.r.t nth term = -1.815e+86 Derivative of radius w.r.t (n-1)th term = 1.344e+84 Derivative of order w.r.t (n-1)th term = 6.87e+84 Derivative of radius w.r.t (n-2)th term = -2.585e+81 Derivative of order w.r.t (n-2)th term = -4.387e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.058e+32 Guess error in order = -9.086e+32 Radius of convergence (six term test) for eq 1 = 1.91e+08 Order of pole (six term test) = -7.13e+14 TOP MAIN SOLVE Loop x[1] = 3 y[1] (analytic) = 20.08553692318768 y[1] (numeric) = 20.08553692318767 absolute error = 3.552713678800501e-15 relative error = 1.768791988178859e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.2 Radius of convergence (three term test) for eq 1 = 5.693e+17 Order of pole (three term test) = 5.693e+17 Derivative of radius w.r.t nth term = 1.643e+89 Derivative of order w.r.t nth term = -1.643e+89 Derivative of radius w.r.t (n-1)th term = 1.217e+87 Derivative of order w.r.t (n-1)th term = 6.221e+87 Derivative of radius w.r.t (n-2)th term = -2.341e+84 Derivative of order w.r.t (n-2)th term = -3.252e+188 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.062e+35 Guess error in order = -9.092e+35 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.100000000000001 y[1] (analytic) = 22.19795128144165 y[1] (numeric) = 22.19795128144164 absolute error = 7.105427357601002e-15 relative error = 3.2009383512529e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.2 Radius of convergence (three term test) for eq 1 = 9.143e+15 Order of pole (three term test) = 9.143e+15 Derivative of radius w.r.t nth term = 4.093e+85 Derivative of order w.r.t nth term = -4.093e+85 Derivative of radius w.r.t (n-1)th term = 3.032e+83 Derivative of order w.r.t (n-1)th term = 1.55e+84 Derivative of radius w.r.t (n-2)th term = -5.831e+80 Derivative of order w.r.t (n-2)th term = -6.632e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.669e+32 Guess error in order = -2.503e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.200000000000001 y[1] (analytic) = 24.53253019710936 y[1] (numeric) = 24.53253019710936 absolute error = 7.105427357601002e-15 relative error = 2.896328793039955e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.3 Radius of convergence (three term test) for eq 1 = 5.177e+15 Order of pole (three term test) = 5.177e+15 Derivative of radius w.r.t nth term = 1.19e+85 Derivative of order w.r.t nth term = -1.19e+85 Derivative of radius w.r.t (n-1)th term = 8.813e+82 Derivative of order w.r.t (n-1)th term = 4.505e+83 Derivative of radius w.r.t (n-2)th term = -1.695e+80 Derivative of order w.r.t (n-2)th term = -1.578e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 5.361e+31 Guess error in order = -8.042e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.300000000000001 y[1] (analytic) = 27.11263892065791 y[1] (numeric) = 27.1126389206579 absolute error = 1.06581410364015e-14 relative error = 3.93106000031622e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.3 Radius of convergence (three term test) for eq 1 = 4.838e+16 Order of pole (three term test) = 4.838e+16 Derivative of radius w.r.t nth term = 9.401e+86 Derivative of order w.r.t nth term = -9.401e+86 Derivative of radius w.r.t (n-1)th term = 6.964e+84 Derivative of order w.r.t (n-1)th term = 3.559e+85 Derivative of radius w.r.t (n-2)th term = -1.339e+82 Derivative of order w.r.t (n-2)th term = -1.021e+186 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.682e+33 Guess error in order = -7.022e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.400000000000001 y[1] (analytic) = 29.96410004739704 y[1] (numeric) = 29.96410004739703 absolute error = 1.06581410364015e-14 relative error = 3.556970180830567e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.3 Radius of convergence (three term test) for eq 1 = 3.002e+16 Order of pole (three term test) = 3.002e+16 Derivative of radius w.r.t nth term = 3.297e+86 Derivative of order w.r.t nth term = -3.297e+86 Derivative of radius w.r.t (n-1)th term = 2.442e+84 Derivative of order w.r.t (n-1)th term = 1.248e+85 Derivative of radius w.r.t (n-2)th term = -4.696e+81 Derivative of order w.r.t (n-2)th term = -2.932e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.814e+33 Guess error in order = -2.722e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.500000000000001 y[1] (analytic) = 33.11545195869234 y[1] (numeric) = 33.11545195869233 absolute error = 1.4210854715202e-14 relative error = 4.291306285938173e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.3 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.600000000000001 y[1] (analytic) = 36.59823444367802 y[1] (numeric) = 36.598234443678 absolute error = 2.131628207280301e-14 relative error = 5.824401749654669e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.4 Radius of convergence (three term test) for eq 1 = 2.423e+16 Order of pole (three term test) = 2.423e+16 Derivative of radius w.r.t nth term = 1.74e+86 Derivative of order w.r.t nth term = -1.74e+86 Derivative of radius w.r.t (n-1)th term = 1.289e+84 Derivative of order w.r.t (n-1)th term = 6.589e+84 Derivative of radius w.r.t (n-2)th term = -2.479e+81 Derivative of order w.r.t (n-2)th term = -1.037e+185 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.17e+33 Guess error in order = -1.755e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.700000000000001 y[1] (analytic) = 40.44730436006743 y[1] (numeric) = 40.44730436006741 absolute error = 2.842170943040401e-14 relative error = 7.026848854348874e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.4 Radius of convergence (three term test) for eq 1 = 1.313e+16 Order of pole (three term test) = 1.313e+16 Derivative of radius w.r.t nth term = 4.641e+85 Derivative of order w.r.t nth term = -4.641e+85 Derivative of radius w.r.t (n-1)th term = 3.438e+83 Derivative of order w.r.t (n-1)th term = 1.757e+84 Derivative of radius w.r.t (n-2)th term = -6.611e+80 Derivative of order w.r.t (n-2)th term = -2.265e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 3.448e+32 Guess error in order = -5.172e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 3.800000000000001 y[1] (analytic) = 44.70118449330087 y[1] (numeric) = 44.70118449330084 absolute error = 2.842170943040401e-14 relative error = 6.358155774297975e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.4 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.176e+08 Order of pole (six term test) = -1.773e+14 TOP MAIN SOLVE Loop x[1] = 3.900000000000001 y[1] (analytic) = 49.40244910553024 y[1] (numeric) = 49.4024491055302 absolute error = 4.263256414560601e-14 relative error = 8.62964588142931e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.5 Radius of convergence (three term test) for eq 1 = 2.233e+16 Order of pole (three term test) = 2.233e+16 Derivative of radius w.r.t nth term = 1.099e+86 Derivative of order w.r.t nth term = -1.099e+86 Derivative of radius w.r.t (n-1)th term = 8.142e+83 Derivative of order w.r.t (n-1)th term = 4.161e+84 Derivative of radius w.r.t (n-2)th term = -1.566e+81 Derivative of order w.r.t (n-2)th term = -3.596e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 9.974e+32 Guess error in order = -1.496e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.000000000000001 y[1] (analytic) = 54.59815003314429 y[1] (numeric) = 54.59815003314426 absolute error = 2.131628207280301e-14 relative error = 3.904213248958576e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.5 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.100000000000001 y[1] (analytic) = 60.340287597362 y[1] (numeric) = 60.340287597362 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.5 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.2 y[1] (analytic) = 66.68633104092515 y[1] (numeric) = 66.68633104092518 absolute error = 2.842170943040401e-14 relative error = 4.261999271329189e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.6 Radius of convergence (three term test) for eq 1 = 9.278e+15 Order of pole (three term test) = 9.278e+15 Derivative of radius w.r.t nth term = 1.403e+85 Derivative of order w.r.t nth term = -1.403e+85 Derivative of radius w.r.t (n-1)th term = 1.04e+83 Derivative of order w.r.t (n-1)th term = 5.313e+83 Derivative of radius w.r.t (n-2)th term = -1.999e+80 Derivative of order w.r.t (n-2)th term = -2.52e+183 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.719e+32 Guess error in order = -2.578e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.3 y[1] (analytic) = 73.69979369959579 y[1] (numeric) = 73.69979369959584 absolute error = 5.684341886080801e-14 relative error = 7.712832832681291e-14 % Correct digits = 16 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.6 Radius of convergence (three term test) for eq 1 = 2.123e+16 Order of pole (three term test) = 2.123e+16 Derivative of radius w.r.t nth term = 6.657e+85 Derivative of order w.r.t nth term = -6.657e+85 Derivative of radius w.r.t (n-1)th term = 4.931e+83 Derivative of order w.r.t (n-1)th term = 2.52e+84 Derivative of radius w.r.t (n-2)th term = -9.483e+80 Derivative of order w.r.t (n-2)th term = -9.785e+183 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 9.011e+32 Guess error in order = -1.352e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.399999999999999 y[1] (analytic) = 81.45086866496807 y[1] (numeric) = 81.45086866496817 absolute error = 9.947598300641403e-14 relative error = 1.221300455561606e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.6 Radius of convergence (three term test) for eq 1 = 3.495e+16 Order of pole (three term test) = 3.495e+16 Derivative of radius w.r.t nth term = 1.633e+86 Derivative of order w.r.t nth term = -1.633e+86 Derivative of radius w.r.t (n-1)th term = 1.21e+84 Derivative of order w.r.t (n-1)th term = 6.184e+84 Derivative of radius w.r.t (n-2)th term = -2.327e+81 Derivative of order w.r.t (n-2)th term = -1.966e+184 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 2.443e+33 Guess error in order = -3.665e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.499999999999999 y[1] (analytic) = 90.01713130052174 y[1] (numeric) = 90.01713130052187 absolute error = 1.27897692436818e-13 relative error = 1.420815022529792e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.7 Radius of convergence (three term test) for eq 1 = 4.973e+15 Order of pole (three term test) = 4.973e+15 Derivative of radius w.r.t nth term = 2.992e+84 Derivative of order w.r.t nth term = -2.992e+84 Derivative of radius w.r.t (n-1)th term = 2.216e+82 Derivative of order w.r.t (n-1)th term = 1.133e+83 Derivative of radius w.r.t (n-2)th term = -4.262e+79 Derivative of order w.r.t (n-2)th term = -2.948e+182 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.946e+31 Guess error in order = -7.42e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.599999999999999 y[1] (analytic) = 99.48431564193369 y[1] (numeric) = 99.48431564193388 absolute error = 1.84741111297626e-13 relative error = 1.856987306044811e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.7 Radius of convergence (three term test) for eq 1 = 1.524e+16 Order of pole (three term test) = 1.524e+16 Derivative of radius w.r.t nth term = 2.541e+85 Derivative of order w.r.t nth term = -2.541e+85 Derivative of radius w.r.t (n-1)th term = 1.882e+83 Derivative of order w.r.t (n-1)th term = 9.62e+83 Derivative of radius w.r.t (n-2)th term = -3.62e+80 Derivative of order w.r.t (n-2)th term = -2.05e+183 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 4.643e+32 Guess error in order = -6.964e+32 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.699999999999998 y[1] (analytic) = 109.9471724521233 y[1] (numeric) = 109.9471724521236 absolute error = 2.415845301584341e-13 relative error = 2.197278245273951e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.7 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.799999999999998 y[1] (analytic) = 121.5104175187346 y[1] (numeric) = 121.510417518735 absolute error = 3.126388037344441e-13 relative error = 2.572938272442698e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.8 Radius of convergence (three term test) for eq 1 = 5.647e+15 Order of pole (three term test) = 5.647e+15 Derivative of radius w.r.t nth term = 2.854e+84 Derivative of order w.r.t nth term = -2.854e+84 Derivative of radius w.r.t (n-1)th term = 2.114e+82 Derivative of order w.r.t (n-1)th term = 1.081e+83 Derivative of radius w.r.t (n-2)th term = -4.066e+79 Derivative of order w.r.t (n-2)th term = -1.543e+182 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 6.37e+31 Guess error in order = -9.555e+31 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.899999999999998 y[1] (analytic) = 134.2897796849352 y[1] (numeric) = 134.2897796849356 absolute error = 3.979039320256561e-13 relative error = 2.963024684076487e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.8 Radius of convergence (three term test) for eq 1 = 2.484e+16 Order of pole (three term test) = 2.484e+16 Derivative of radius w.r.t nth term = 5.003e+85 Derivative of order w.r.t nth term = -5.003e+85 Derivative of radius w.r.t (n-1)th term = 3.706e+83 Derivative of order w.r.t (n-1)th term = 1.894e+84 Derivative of radius w.r.t (n-2)th term = -7.126e+80 Derivative of order w.r.t (n-2)th term = -2.215e+183 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.234e+33 Guess error in order = -1.851e+33 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 4.999999999999997 y[1] (analytic) = 148.4131591025762 y[1] (numeric) = 148.4131591025767 absolute error = 5.115907697472721e-13 relative error = 3.447071491778466e-13 % Correct digits = 15 h = 0.1 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19 Order of pole (ratio test) = 128.8 Radius of convergence (three term test) for eq 1 = 9.067e+15 Order of pole (three term test) = 9.067e+15 Derivative of radius w.r.t nth term = 6.024e+84 Derivative of order w.r.t nth term = -6.024e+84 Derivative of radius w.r.t (n-1)th term = 4.462e+82 Derivative of order w.r.t (n-1)th term = 2.281e+83 Derivative of radius w.r.t (n-2)th term = -8.581e+79 Derivative of order w.r.t (n-2)th term = -2.184e+182 Guess at Error should be multiplied by ratio of error in relevant terms (I used value of term instead of error in term). Guess error in radius = 1.642e+32 Guess error in order = -2.463e+32 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = y; Iterations = 101 Total Elapsed Time = 0 Seconds Elapsed Time(since restart) = 0 Seconds Time to Timeout = 3 Minutes 0 Seconds Percent Done = 102 %