##############ECHO OF PROBLEM################# ##############temp/sin_sqrt_linpostode.ode################# diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=40; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=2.0; x_end=3.0; array_y_init[0 + 1] = exact_soln_y(x_start); glob_look_poles=true; glob_upper_ratio_limit=1.001; glob_lower_ratio_limit=0.999; glob_type_given_pole=1; array_given_rad_poles[1][1]=-1.5; array_given_rad_poles[1][2]=0.0; array_given_ord_poles[1][1]=0.5; array_given_ord_poles[1][2]=0.0; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=100000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y (double x) { return(sin(sqrt(2.0*x+3.0))-sqrt(2.0*x+3.0)*cos(sqrt(2.0*x+3.0))); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1 estimated_steps = 1000000 step_error = 2.5e-15 est_needed_step_err = 2.5e-15 opt_iter = 1 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 1000000 step_error = 7.00722992397755e-15 est_needed_step_err = 7.00722992397755e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.791154658409449e-240 estimated_step_error = 1.791154658409449e-240 Double H and LOOP opt_iter = 2 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 2e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 500000 step_error = 9.909719593155643e-15 est_needed_step_err = 9.909719593155643e-15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.230871943468012e-229 estimated_step_error = 1.230871943468012e-229 Double H and LOOP opt_iter = 3 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 4e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 250000 step_error = 1.40144598479551e-14 est_needed_step_err = 1.40144598479551e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.45848531622724e-219 estimated_step_error = 8.45848531622724e-219 Double H and LOOP opt_iter = 4 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 8e-06 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 125000 step_error = 1.981943918631129e-14 est_needed_step_err = 1.981943918631129e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.812623726234864e-208 estimated_step_error = 5.812623726234864e-208 Double H and LOOP opt_iter = 5 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 1.6e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 62500 step_error = 2.80289196959102e-14 est_needed_step_err = 2.80289196959102e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.994400317271163e-197 estimated_step_error = 3.994400317271163e-197 Double H and LOOP opt_iter = 6 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 3.2e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 31250 step_error = 3.963887837262257e-14 est_needed_step_err = 3.963887837262257e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.744925097867764e-186 estimated_step_error = 2.744925097867764e-186 Double H and LOOP opt_iter = 7 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 6.4e-05 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 15625 step_error = 5.60578393918204e-14 est_needed_step_err = 5.60578393918204e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.886290056712885e-175 estimated_step_error = 1.886290056712885e-175 Double H and LOOP opt_iter = 8 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.000128 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 7812.5 step_error = 7.927775674524514e-14 est_needed_step_err = 7.927775674524514e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.296237514201058e-164 estimated_step_error = 1.296237514201058e-164 Double H and LOOP opt_iter = 9 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.000256 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 3906.25 step_error = 1.121156787836408e-13 est_needed_step_err = 1.121156787836408e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.907523232812964e-154 estimated_step_error = 8.907523232812964e-154 Double H and LOOP opt_iter = 10 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.000512 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 1953.125 step_error = 1.585555134904903e-13 est_needed_step_err = 1.585555134904903e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.120992896246427e-143 estimated_step_error = 6.120992896246427e-143 Double H and LOOP opt_iter = 11 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.001024 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 976.5625 step_error = 2.242313575672816e-13 est_needed_step_err = 2.242313575672816e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.206025065914012e-132 estimated_step_error = 4.206025065914012e-132 Double H and LOOP opt_iter = 12 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.002048 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 488.28125 step_error = 3.171110269809806e-13 est_needed_step_err = 3.171110269809806e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.88996099311406e-121 estimated_step_error = 2.88996099311406e-121 Double H and LOOP opt_iter = 13 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.004096 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 244.140625 step_error = 4.484627151345632e-13 est_needed_step_err = 4.484627151345632e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.985420083100941e-110 estimated_step_error = 1.985420083100941e-110 Double H and LOOP opt_iter = 14 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 min_size = 2.80289196959102 glob_desired_digits_correct = 10 estimated_h = 0.008192 estimated_answer = 2.80289196959102 desired_abs_gbl_error = 2.80289196959102e-10 range = 1 estimated_steps = 122.0703125 step_error = 6.342220539619611e-13 est_needed_step_err = 6.342220539619611e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.36362050960644e-99 estimated_step_error = 1.36362050960644e-99 Double H and LOOP opt_iter = 15 SETTING H FOR DISPLAY INTERVAL Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 2.441 Order of pole (six term test) = -1.313 START of Soultion TOP MAIN SOLVE Loop x[1] = 2 y[1] (analytic) = 2.80289196959102 y[1] (numeric) = 2.80289196959102 absolute error = 0 relative error = 0 % Desired digits = 10 Estimated correct digits = 13 Correct digits = 16 h = 0.01 Radius of convergence (given) for eq 1 = 3.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4 Order of pole (six term test) = -1.313 TOP MAIN SOLVE Loop x[1] = 2.01 y[1] (analytic) = 2.807633062296782 y[1] (numeric) = 2.80764969587945 absolute error = 1.663358266812409e-05 relative error = 0.0005924414729080375 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 6 h = 0.01 Radius of convergence (given) for eq 1 = 3.51 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.007 Order of pole (six term test) = -1.315 TOP MAIN SOLVE Loop x[1] = 2.02 y[1] (analytic) = 2.812340890281376 y[1] (numeric) = 2.812374167432905 absolute error = 3.327715152900979e-05 relative error = 0.001183254549404229 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.52 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.014 Order of pole (six term test) = -1.317 TOP MAIN SOLVE Loop x[1] = 2.029999999999999 y[1] (analytic) = 2.817015433909019 y[1] (numeric) = 2.817065364336703 absolute error = 4.993042768441924e-05 relative error = 0.001772458435385053 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.53 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.021 Order of pole (six term test) = -1.318 TOP MAIN SOLVE Loop x[1] = 2.039999999999999 y[1] (analytic) = 2.821656674099208 y[1] (numeric) = 2.821723267233281 absolute error = 6.659313407331169e-05 relative error = 0.002360072176200212 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.54 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.028 Order of pole (six term test) = -1.32 TOP MAIN SOLVE Loop x[1] = 2.049999999999999 y[1] (analytic) = 2.826264592323069 y[1] (numeric) = 2.826347857318528 absolute error = 8.326499545940891e-05 relative error = 0.002946114659100924 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.55 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.035 Order of pole (six term test) = -1.322 TOP MAIN SOLVE Loop x[1] = 2.059999999999999 y[1] (analytic) = 2.830839170599731 y[1] (numeric) = 2.830939116338147 absolute error = 9.994573841520804e-05 relative error = 0.003530604615522326 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.56 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.042 Order of pole (six term test) = -1.323 TOP MAIN SOLVE Loop x[1] = 2.069999999999999 y[1] (analytic) = 2.835380391492727 y[1] (numeric) = 2.835497026584036 absolute error = 0.0001166350913086589 relative error = 0.004113560623421489 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.57 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.049 Order of pole (six term test) = -1.325 TOP MAIN SOLVE Loop x[1] = 2.079999999999998 y[1] (analytic) = 2.83988823810642 y[1] (numeric) = 2.840021570890711 absolute error = 0.0001333327842911736 relative error = 0.004695001109623848 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.58 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.056 Order of pole (six term test) = -1.327 TOP MAIN SOLVE Loop x[1] = 2.089999999999998 y[1] (analytic) = 2.844362694082465 y[1] (numeric) = 2.844512732631745 absolute error = 0.0001500385492803069 relative error = 0.005274944351944062 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.59 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.063 Order of pole (six term test) = -1.329 TOP MAIN SOLVE Loop x[1] = 2.099999999999998 y[1] (analytic) = 2.848803743596289 y[1] (numeric) = 2.848970495716238 absolute error = 0.0001667521199490984 relative error = 0.005853408481505047 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.6 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.07 Order of pole (six term test) = -1.33 TOP MAIN SOLVE Loop x[1] = 2.109999999999998 y[1] (analytic) = 2.853211371353604 y[1] (numeric) = 2.853394844585316 absolute error = 0.0001834732317118615 relative error = 0.006430411484895321 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.61 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.077 Order of pole (six term test) = -1.332 TOP MAIN SOLVE Loop x[1] = 2.119999999999997 y[1] (analytic) = 2.857585562586943 y[1] (numeric) = 2.857785764208655 absolute error = 0.0002002016217117486 relative error = 0.007005971206353244 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.62 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.084 Order of pole (six term test) = -1.334 TOP MAIN SOLVE Loop x[1] = 2.129999999999997 y[1] (analytic) = 2.861926303052224 y[1] (numeric) = 2.862143240081028 absolute error = 0.0002169370288043204 relative error = 0.007580105349776429 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.63 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.091 Order of pole (six term test) = -1.335 TOP MAIN SOLVE Loop x[1] = 2.139999999999997 y[1] (analytic) = 2.866233579025337 y[1] (numeric) = 2.866467258218888 absolute error = 0.0002336791935504401 relative error = 0.008152831481023354 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.64 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.098 Order of pole (six term test) = -1.337 TOP MAIN SOLVE Loop x[1] = 2.149999999999997 y[1] (analytic) = 2.870507377298762 y[1] (numeric) = 2.87075780515696 absolute error = 0.0002504278581980657 relative error = 0.008724167029792698 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.65 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.105 Order of pole (six term test) = -1.339 TOP MAIN SOLVE Loop x[1] = 2.159999999999997 y[1] (analytic) = 2.874747685178208 y[1] (numeric) = 2.875014867944879 absolute error = 0.0002671827666711479 relative error = 0.009294129291718519 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.66 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.112 Order of pole (six term test) = -1.34 TOP MAIN SOLVE Loop x[1] = 2.169999999999996 y[1] (analytic) = 2.878954490479277 y[1] (numeric) = 2.879238434143838 absolute error = 0.0002839436645607485 relative error = 0.00986273543050966 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 5 h = 0.01 Radius of convergence (given) for eq 1 = 3.67 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.118 Order of pole (six term test) = -1.342 TOP MAIN SOLVE Loop x[1] = 2.179999999999996 y[1] (analytic) = 2.883127781524157 y[1] (numeric) = 2.883428491823263 absolute error = 0.0003007102991063881 relative error = 0.01043000247971731 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.68 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.125 Order of pole (six term test) = -1.344 TOP MAIN SOLVE Loop x[1] = 2.189999999999996 y[1] (analytic) = 2.887267547138336 y[1] (numeric) = 2.887585029557524 absolute error = 0.0003174824191880532 relative error = 0.01099594734484237 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.69 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.132 Order of pole (six term test) = -1.345 TOP MAIN SOLVE Loop x[1] = 2.199999999999996 y[1] (analytic) = 2.89137377664734 y[1] (numeric) = 2.891708036422653 absolute error = 0.0003342597753137611 relative error = 0.01156058680525727 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.7 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.139 Order of pole (six term test) = -1.347 TOP MAIN SOLVE Loop x[1] = 2.209999999999996 y[1] (analytic) = 2.895446459873497 y[1] (numeric) = 2.895797501993102 absolute error = 0.0003510421196049052 relative error = 0.01212393751602101 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.71 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.146 Order of pole (six term test) = -1.349 TOP MAIN SOLVE Loop x[1] = 2.219999999999995 y[1] (analytic) = 2.899485587132728 y[1] (numeric) = 2.899853416338515 absolute error = 0.0003678292057869292 relative error = 0.01268601600984924 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.72 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.152 Order of pole (six term test) = -1.35 TOP MAIN SOLVE Loop x[1] = 2.229999999999995 y[1] (analytic) = 2.903491149231351 y[1] (numeric) = 2.903875770020528 absolute error = 0.0003846207891773368 relative error = 0.01324683869896275 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.73 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.159 Order of pole (six term test) = -1.352 TOP MAIN SOLVE Loop x[1] = 2.239999999999995 y[1] (analytic) = 2.907463137462918 y[1] (numeric) = 2.907864554089592 absolute error = 0.0004014166266737007 relative error = 0.01380642187690747 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.74 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.166 Order of pole (six term test) = -1.354 TOP MAIN SOLVE Loop x[1] = 2.249999999999995 y[1] (analytic) = 2.911401543605079 y[1] (numeric) = 2.911819760081818 absolute error = 0.0004182164767390084 relative error = 0.01436478172025514 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.75 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.172 Order of pole (six term test) = -1.355 TOP MAIN SOLVE Loop x[1] = 2.259999999999994 y[1] (analytic) = 2.91530635991645 y[1] (numeric) = 2.915741380015847 absolute error = 0.0004350200993976649 relative error = 0.01492193429064286 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.76 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.179 Order of pole (six term test) = -1.357 TOP MAIN SOLVE Loop x[1] = 2.269999999999994 y[1] (analytic) = 2.919177579133526 y[1] (numeric) = 2.919629406389741 absolute error = 0.0004518272562146208 relative error = 0.01547789553620553 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.77 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.186 Order of pole (six term test) = -1.358 TOP MAIN SOLVE Loop x[1] = 2.279999999999994 y[1] (analytic) = 2.923015194467601 y[1] (numeric) = 2.923483832177896 absolute error = 0.0004686377102940398 relative error = 0.01603268129365292 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.78 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.192 Order of pole (six term test) = -1.36 TOP MAIN SOLVE Loop x[1] = 2.289999999999994 y[1] (analytic) = 2.926819199601719 y[1] (numeric) = 2.927304650827979 absolute error = 0.0004854512262602029 relative error = 0.01658630728971106 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.79 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.199 Order of pole (six term test) = -1.362 TOP MAIN SOLVE Loop x[1] = 2.299999999999994 y[1] (analytic) = 2.93058958868764 y[1] (numeric) = 2.931091856257891 absolute error = 0.0005022675702504031 relative error = 0.01713878914294941 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.8 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.206 Order of pole (six term test) = -1.363 TOP MAIN SOLVE Loop x[1] = 2.309999999999993 y[1] (analytic) = 2.934326356342834 y[1] (numeric) = 2.934845442852738 absolute error = 0.0005190865099038433 relative error = 0.01769014236544571 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.81 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.212 Order of pole (six term test) = -1.365 TOP MAIN SOLVE Loop x[1] = 2.319999999999993 y[1] (analytic) = 2.938029497647494 y[1] (numeric) = 2.938565405461843 absolute error = 0.0005359078143492013 relative error = 0.01824038236438087 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.82 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.219 Order of pole (six term test) = -1.366 TOP MAIN SOLVE Loop x[1] = 2.329999999999993 y[1] (analytic) = 2.941699008141566 y[1] (numeric) = 2.942251739395764 absolute error = 0.0005527312541975249 relative error = 0.01878952444379127 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.83 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.225 Order of pole (six term test) = -1.368 TOP MAIN SOLVE Loop x[1] = 2.339999999999993 y[1] (analytic) = 2.945334883821811 y[1] (numeric) = 2.945904440423338 absolute error = 0.0005695566015271325 relative error = 0.01933758380602502 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.84 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.232 Order of pole (six term test) = -1.37 TOP MAIN SOLVE Loop x[1] = 2.349999999999993 y[1] (analytic) = 2.948937121138875 y[1] (numeric) = 2.949523504768752 absolute error = 0.0005863836298765079 relative error = 0.01988457555344712 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.85 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.239 Order of pole (six term test) = -1.371 TOP MAIN SOLVE Loop x[1] = 2.359999999999992 y[1] (analytic) = 2.95250571699439 y[1] (numeric) = 2.953108929108623 absolute error = 0.0006032121142331981 relative error = 0.02043051468998542 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.86 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.245 Order of pole (six term test) = -1.373 TOP MAIN SOLVE Loop x[1] = 2.369999999999992 y[1] (analytic) = 2.956040668738087 y[1] (numeric) = 2.95666071056911 absolute error = 0.0006200418310227107 relative error = 0.02097541612265443 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.87 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.252 Order of pole (six term test) = -1.374 TOP MAIN SOLVE Loop x[1] = 2.379999999999992 y[1] (analytic) = 2.959541974164942 y[1] (numeric) = 2.96017884672304 absolute error = 0.0006368725580983003 relative error = 0.02151929466308715 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.88 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.258 Order of pole (six term test) = -1.376 TOP MAIN SOLVE Loop x[1] = 2.389999999999992 y[1] (analytic) = 2.963009631512322 y[1] (numeric) = 2.963663335587056 absolute error = 0.0006537040747338629 relative error = 0.02206216502915017 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.89 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.265 Order of pole (six term test) = -1.377 TOP MAIN SOLVE Loop x[1] = 2.399999999999991 y[1] (analytic) = 2.966443639457173 y[1] (numeric) = 2.967114175618783 absolute error = 0.0006705361616092809 relative error = 0.02260404184628236 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.9 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.271 Order of pole (six term test) = -1.379 TOP MAIN SOLVE Loop x[1] = 2.409999999999991 y[1] (analytic) = 2.969843997113212 y[1] (numeric) = 2.970531365714017 absolute error = 0.0006873686008050939 relative error = 0.02314493964912767 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.91 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.278 Order of pole (six term test) = -1.38 TOP MAIN SOLVE Loop x[1] = 2.419999999999991 y[1] (analytic) = 2.973210704028145 y[1] (numeric) = 2.973914905203934 absolute error = 0.0007042011757887323 relative error = 0.02368487288286267 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.92 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.284 Order of pole (six term test) = -1.382 TOP MAIN SOLVE Loop x[1] = 2.429999999999991 y[1] (analytic) = 2.976543760180903 y[1] (numeric) = 2.977264793852312 absolute error = 0.0007210336714091881 relative error = 0.02422385590478826 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.93 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.291 Order of pole (six term test) = -1.383 TOP MAIN SOLVE Loop x[1] = 2.439999999999991 y[1] (analytic) = 2.979843165978899 y[1] (numeric) = 2.980581031852783 absolute error = 0.0007378658738836918 relative error = 0.02476190298563239 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.94 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.297 Order of pole (six term test) = -1.385 TOP MAIN SOLVE Loop x[1] = 2.44999999999999 y[1] (analytic) = 2.9831089222553 y[1] (numeric) = 2.983863619826089 absolute error = 0.0007546975707892756 relative error = 0.025299028310998 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.95 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.304 Order of pole (six term test) = -1.386 TOP MAIN SOLVE Loop x[1] = 2.45999999999999 y[1] (analytic) = 2.986341030266322 y[1] (numeric) = 2.987112558817377 absolute error = 0.0007715285510556669 relative error = 0.02583524598283612 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.96 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.31 Order of pole (six term test) = -1.388 TOP MAIN SOLVE Loop x[1] = 2.46999999999999 y[1] (analytic) = 2.989539491688539 y[1] (numeric) = 2.990327850293492 absolute error = 0.0007883586049528546 relative error = 0.02637057002072173 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.97 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.316 Order of pole (six term test) = -1.389 TOP MAIN SOLVE Loop x[1] = 2.47999999999999 y[1] (analytic) = 2.992704308616217 y[1] (numeric) = 2.9935094961403 absolute error = 0.0008051875240830952 relative error = 0.02690501436326004 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.98 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.323 Order of pole (six term test) = -1.391 TOP MAIN SOLVE Loop x[1] = 2.48999999999999 y[1] (analytic) = 2.995835483558659 y[1] (numeric) = 2.996657498660033 absolute error = 0.0008220151013733634 relative error = 0.02743859286948953 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 3.99 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.329 Order of pole (six term test) = -1.392 TOP MAIN SOLVE Loop x[1] = 2.499999999999989 y[1] (analytic) = 2.998933019437574 y[1] (numeric) = 2.999771860568637 absolute error = 0.0008388411310633614 relative error = 0.02797131932011871 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.336 Order of pole (six term test) = -1.394 TOP MAIN SOLVE Loop x[1] = 2.509999999999989 y[1] (analytic) = 3.001996919584457 y[1] (numeric) = 3.002852584993156 absolute error = 0.000855665408698858 relative error = 0.0285032074189237 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.01 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.342 Order of pole (six term test) = -1.395 TOP MAIN SOLVE Loop x[1] = 2.519999999999989 y[1] (analytic) = 3.005027187737997 y[1] (numeric) = 3.00589967546912 absolute error = 0.0008724877311223622 relative error = 0.02903427079403958 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.02 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.348 Order of pole (six term test) = -1.397 TOP MAIN SOLVE Loop x[1] = 2.529999999999989 y[1] (analytic) = 3.008023828041493 y[1] (numeric) = 3.008913135937957 absolute error = 0.0008893078964637979 relative error = 0.02956452299923506 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.03 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.355 Order of pole (six term test) = -1.398 TOP MAIN SOLVE Loop x[1] = 2.539999999999988 y[1] (analytic) = 3.010986845040289 y[1] (numeric) = 3.011892970744422 absolute error = 0.0009061257041333981 relative error = 0.03009397751524463 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.04 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.361 Order of pole (six term test) = -1.399 TOP MAIN SOLVE Loop x[1] = 2.549999999999988 y[1] (analytic) = 3.013916243679235 y[1] (numeric) = 3.014839184634044 absolute error = 0.0009229409548092704 relative error = 0.03062264775090735 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.05 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.367 Order of pole (six term test) = -1.401 TOP MAIN SOLVE Loop x[1] = 2.559999999999988 y[1] (analytic) = 3.016812029300151 y[1] (numeric) = 3.017751782750584 absolute error = 0.0009397534504334004 relative error = 0.03115054704457033 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.06 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.374 Order of pole (six term test) = -1.402 TOP MAIN SOLVE Loop x[1] = 2.569999999999988 y[1] (analytic) = 3.01967420763932 y[1] (numeric) = 3.020630770633521 absolute error = 0.0009565629942014375 relative error = 0.03167768866526983 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.07 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.38 Order of pole (six term test) = -1.404 TOP MAIN SOLVE Loop x[1] = 2.579999999999988 y[1] (analytic) = 3.02250278482499 y[1] (numeric) = 3.023476154215543 absolute error = 0.0009733693905538132 relative error = 0.03220408581394157 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.08 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.386 Order of pole (six term test) = -1.405 TOP MAIN SOLVE Loop x[1] = 2.589999999999987 y[1] (analytic) = 3.025297767374898 y[1] (numeric) = 3.026287939820065 absolute error = 0.0009901724451668592 relative error = 0.03272975162461606 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.09 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.393 Order of pole (six term test) = -1.407 TOP MAIN SOLVE Loop x[1] = 2.599999999999987 y[1] (analytic) = 3.028059162193808 y[1] (numeric) = 3.029066134158755 absolute error = 0.001006971964947034 relative error = 0.03325469916570223 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.1 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.399 Order of pole (six term test) = -1.408 TOP MAIN SOLVE Loop x[1] = 2.609999999999987 y[1] (analytic) = 3.030786976571064 y[1] (numeric) = 3.031810744329084 absolute error = 0.001023767758020711 relative error = 0.03377894144110943 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.405 Order of pole (six term test) = -1.409 TOP MAIN SOLVE Loop x[1] = 2.619999999999987 y[1] (analytic) = 3.033481218178158 y[1] (numeric) = 3.034521777811884 absolute error = 0.001040559633726623 relative error = 0.03430249139144367 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.12 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.412 Order of pole (six term test) = -1.411 TOP MAIN SOLVE Loop x[1] = 2.629999999999987 y[1] (analytic) = 3.036141895066324 y[1] (numeric) = 3.037199242468932 absolute error = 0.001057347402607878 relative error = 0.0348253618951752 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.13 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.418 Order of pole (six term test) = -1.412 TOP MAIN SOLVE Loop x[1] = 2.639999999999986 y[1] (analytic) = 3.038769015664134 y[1] (numeric) = 3.039843146540538 absolute error = 0.0010741308764044 relative error = 0.03534756576980712 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.14 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.424 Order of pole (six term test) = -1.413 TOP MAIN SOLVE Loop x[1] = 2.649999999999986 y[1] (analytic) = 3.041362588775117 y[1] (numeric) = 3.042453498643163 absolute error = 0.001090909868045387 relative error = 0.03586911577303057 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.15 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.431 Order of pole (six term test) = -1.415 TOP MAIN SOLVE Loop x[1] = 2.659999999999986 y[1] (analytic) = 3.043922623575397 y[1] (numeric) = 3.045030307767037 absolute error = 0.001107684191639535 relative error = 0.03639002460379388 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.16 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.437 Order of pole (six term test) = -1.416 TOP MAIN SOLVE Loop x[1] = 2.669999999999986 y[1] (analytic) = 3.046449129611337 y[1] (numeric) = 3.047573583273806 absolute error = 0.001124453662469715 relative error = 0.03691030490350489 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.443 Order of pole (six term test) = -1.418 TOP MAIN SOLVE Loop x[1] = 2.679999999999986 y[1] (analytic) = 3.048942116797203 y[1] (numeric) = 3.050083334894189 absolute error = 0.001141218096985419 relative error = 0.03742996925714762 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.18 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.449 Order of pole (six term test) = -1.419 TOP MAIN SOLVE Loop x[1] = 2.689999999999985 y[1] (analytic) = 3.051401595412852 y[1] (numeric) = 3.052559572725644 absolute error = 0.001157977312791658 relative error = 0.03794903019426995 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.19 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.456 Order of pole (six term test) = -1.42 TOP MAIN SOLVE Loop x[1] = 2.699999999999985 y[1] (analytic) = 3.053827576101416 y[1] (numeric) = 3.055002307230062 absolute error = 0.001174731128645856 relative error = 0.03846750019022174 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.2 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.462 Order of pole (six term test) = -1.421 TOP MAIN SOLVE Loop x[1] = 2.709999999999985 y[1] (analytic) = 3.056220069867019 y[1] (numeric) = 3.057411549231467 absolute error = 0.001191479364448078 relative error = 0.03898539166716228 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.21 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.468 Order of pole (six term test) = -1.423 TOP MAIN SOLVE Loop x[1] = 2.719999999999985 y[1] (analytic) = 3.058579088072495 y[1] (numeric) = 3.059787309913729 absolute error = 0.001208221841234369 relative error = 0.03950271699515823 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.22 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.475 Order of pole (six term test) = -1.424 TOP MAIN SOLVE Loop x[1] = 2.729999999999984 y[1] (analytic) = 3.060904642437134 y[1] (numeric) = 3.062129600818304 absolute error = 0.001224958381169206 relative error = 0.0400194884932409 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.23 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.481 Order of pole (six term test) = -1.425 TOP MAIN SOLVE Loop x[1] = 2.739999999999984 y[1] (analytic) = 3.063196745034432 y[1] (numeric) = 3.06443843384197 absolute error = 0.001241688807537944 relative error = 0.04053571843045252 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.24 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.487 Order of pole (six term test) = -1.427 TOP MAIN SOLVE Loop x[1] = 2.749999999999984 y[1] (analytic) = 3.065455408289858 y[1] (numeric) = 3.066713821234597 absolute error = 0.001258412944739717 relative error = 0.04105141902689608 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.25 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.493 Order of pole (six term test) = -1.428 TOP MAIN SOLVE Loop x[1] = 2.759999999999984 y[1] (analytic) = 3.067680644978635 y[1] (numeric) = 3.068955775596915 absolute error = 0.001275130618280329 relative error = 0.04156660245477442 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.26 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.5 Order of pole (six term test) = -1.429 TOP MAIN SOLVE Loop x[1] = 2.769999999999984 y[1] (analytic) = 3.069872468223541 y[1] (numeric) = 3.071164309878308 absolute error = 0.001291841654767811 relative error = 0.04208128083950563 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.506 Order of pole (six term test) = -1.43 TOP MAIN SOLVE Loop x[1] = 2.779999999999983 y[1] (analytic) = 3.072030891492715 y[1] (numeric) = 3.073339437374614 absolute error = 0.001308545881899548 relative error = 0.04259546626055309 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.28 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.512 Order of pole (six term test) = -1.432 TOP MAIN SOLVE Loop x[1] = 2.789999999999983 y[1] (analytic) = 3.074155928597481 y[1] (numeric) = 3.075481171725944 absolute error = 0.001325243128462272 relative error = 0.04310917075266531 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.29 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.519 Order of pole (six term test) = -1.433 TOP MAIN SOLVE Loop x[1] = 2.799999999999983 y[1] (analytic) = 3.076247593690192 y[1] (numeric) = 3.077589526914511 absolute error = 0.001341933224319192 relative error = 0.04362240630668617 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.3 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.525 Order of pole (six term test) = -1.434 TOP MAIN SOLVE Loop x[1] = 2.809999999999983 y[1] (analytic) = 3.078305901262071 y[1] (numeric) = 3.079664517262477 absolute error = 0.001358616000406876 relative error = 0.04413518487067379 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.531 Order of pole (six term test) = -1.435 TOP MAIN SOLVE Loop x[1] = 2.819999999999983 y[1] (analytic) = 3.080330866141084 y[1] (numeric) = 3.081706157429812 absolute error = 0.001375291288728153 relative error = 0.04464751835087973 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.537 Order of pole (six term test) = -1.437 TOP MAIN SOLVE Loop x[1] = 2.829999999999982 y[1] (analytic) = 3.082322503489818 y[1] (numeric) = 3.083714462412162 absolute error = 0.001391958922343672 relative error = 0.0451594186126757 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.544 Order of pole (six term test) = -1.438 TOP MAIN SOLVE Loop x[1] = 2.839999999999982 y[1] (analytic) = 3.084280828803368 y[1] (numeric) = 3.085689447538734 absolute error = 0.001408618735366129 relative error = 0.04567089748155786 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.34 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.55 Order of pole (six term test) = -1.439 TOP MAIN SOLVE Loop x[1] = 2.849999999999982 y[1] (analytic) = 3.086205857907247 y[1] (numeric) = 3.087631128470201 absolute error = 0.001425270562953607 relative error = 0.04618196674411347 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.556 Order of pole (six term test) = -1.44 TOP MAIN SOLVE Loop x[1] = 2.859999999999982 y[1] (analytic) = 3.088097606955299 y[1] (numeric) = 3.089539521196606 absolute error = 0.001441914241306463 relative error = 0.04669263814909382 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.36 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.563 Order of pole (six term test) = -1.442 TOP MAIN SOLVE Loop x[1] = 2.869999999999981 y[1] (analytic) = 3.089956092427637 y[1] (numeric) = 3.091414642035289 absolute error = 0.001458549607652682 relative error = 0.04720292340810468 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.37 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.569 Order of pole (six term test) = -1.443 TOP MAIN SOLVE Loop x[1] = 2.879999999999981 y[1] (analytic) = 3.091781331128576 y[1] (numeric) = 3.093256507628827 absolute error = 0.001475176500250974 relative error = 0.04771283419686406 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.38 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.575 Order of pole (six term test) = -1.444 TOP MAIN SOLVE Loop x[1] = 2.889999999999981 y[1] (analytic) = 3.093573340184602 y[1] (numeric) = 3.095065134942979 absolute error = 0.001491794758377019 relative error = 0.04822238215590515 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.39 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.582 Order of pole (six term test) = -1.445 TOP MAIN SOLVE Loop x[1] = 2.899999999999981 y[1] (analytic) = 3.095332137042332 y[1] (numeric) = 3.096840541264654 absolute error = 0.00150840422232168 relative error = 0.04873157889165969 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.4 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.588 Order of pole (six term test) = -1.446 TOP MAIN SOLVE Loop x[1] = 2.909999999999981 y[1] (analytic) = 3.097057739466499 y[1] (numeric) = 3.098582744199881 absolute error = 0.001525004733382129 relative error = 0.04924043597730365 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.41 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.594 Order of pole (six term test) = -1.447 TOP MAIN SOLVE Loop x[1] = 2.91999999999998 y[1] (analytic) = 3.098750165537946 y[1] (numeric) = 3.100291761671803 absolute error = 0.001541596133856959 relative error = 0.04974896495372472 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.601 Order of pole (six term test) = -1.449 TOP MAIN SOLVE Loop x[1] = 2.92999999999998 y[1] (analytic) = 3.100409433651632 y[1] (numeric) = 3.101967611918673 absolute error = 0.001558178267040855 relative error = 0.05025717733046786 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.607 Order of pole (six term test) = -1.45 TOP MAIN SOLVE Loop x[1] = 2.93999999999998 y[1] (analytic) = 3.102035562514651 y[1] (numeric) = 3.103610313491866 absolute error = 0.001574750977215267 relative error = 0.05076508458654491 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.613 Order of pole (six term test) = -1.451 TOP MAIN SOLVE Loop x[1] = 2.94999999999998 y[1] (analytic) = 3.10362857114426 y[1] (numeric) = 3.105219885253907 absolute error = 0.001591314109647524 relative error = 0.05127269817150931 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.62 Order of pole (six term test) = -1.452 TOP MAIN SOLVE Loop x[1] = 2.95999999999998 y[1] (analytic) = 3.105188478865928 y[1] (numeric) = 3.106796346376507 absolute error = 0.001607867510579286 relative error = 0.05178002950618022 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.46 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.626 Order of pole (six term test) = -1.453 TOP MAIN SOLVE Loop x[1] = 2.969999999999979 y[1] (analytic) = 3.106715305311385 y[1] (numeric) = 3.108339716338608 absolute error = 0.001624411027223438 relative error = 0.05228708998363222 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.632 Order of pole (six term test) = -1.454 TOP MAIN SOLVE Loop x[1] = 2.979999999999979 y[1] (analytic) = 3.108209070416688 y[1] (numeric) = 3.109850014924447 absolute error = 0.001640944507758757 relative error = 0.05279389097010681 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.639 Order of pole (six term test) = -1.455 TOP MAIN SOLVE Loop x[1] = 2.989999999999979 y[1] (analytic) = 3.109669794420306 y[1] (numeric) = 3.111327262221629 absolute error = 0.001657467801323254 relative error = 0.05330044380587468 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.49 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.645 Order of pole (six term test) = -1.456 TOP MAIN SOLVE Loop x[1] = 2.999999999999979 y[1] (analytic) = 3.111097497861201 y[1] (numeric) = 3.112771478619208 absolute error = 0.001673980758007065 relative error = 0.05380675980607756 % Desired digits = 10 Estimated correct digits = 12 Correct digits = 4 h = 0.01 Radius of convergence (given) for eq 1 = 4.5 Order of pole (given) = 0.5 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.651 Order of pole (six term test) = -1.457 Finished! diff ( y , x , 1 ) = sin ( sqrt ( 2.0 * x + 3.0 ) ) ; Iterations = 101 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 102 %