|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 2 > ret := 1.0; > else > ret := -1.0; > fi;# end if 2; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y[1]) < min_size) then # if number 2 > min_size := omniabs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > if (min_size < 1.0) then # if number 2 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 2; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y[1]) < min_size then min_size := omniabs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 2 > max_estimated_step_error := est_tmp; > fi;# end if 2; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 2 > ret := true; > else > ret := false; > fi;# end if 2; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 2 > if (iter >= 0) then # if number 3 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 4 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 5 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 5; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 4; > if (glob_iter = 1) then # if number 4 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 4; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 3; > #BOTTOM DISPLAY ALOT > fi;# end if 2; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := omniabs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 3 > glob_normmax := tmp; > fi;# end if 3 > fi;# end if 2; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 2 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 3 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 3 > fi;# end if 2; > if ( not glob_reached_optimal_h) then # if number 2 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 2; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y_higher[1, 1]) then tmp := omniabs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 2 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 2; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y_higher[1,n]) = 0.0) or (omniabs(array_y_higher[1,n+1]) = 0.0)) then # if number 2 > found_sing := 0; > else > tmp_rad := omniabs(array_y_higher[1,n] * glob_h / array_y_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 3 > if (tmp_rad < rad_c) then # if number 4 > rad_c := tmp_rad; > fi;# end if 4; > elif > (cnt = 0) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5 > fi;# end if 4; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 4 > if (rad_c < array_pole[1]) then # if number 5 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 5; > fi;# end if 4; > #BOTTOM radius ratio test in Henrici1 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y_higher[1,m]) = 0.0) or (omniabs(array_y_higher[1,m-1]) = 0.0) or (omniabs(array_y_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 4 > rm0 := array_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 5 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 5 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 4; > #BOTTOM RADII REAL EQ = 1 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y_higher[1,n]) <> 0.0) then # if number 4 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 4; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 5 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 6 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 7 > if (rcs > 0.0) then # if number 8 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 8 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > fi;# end if 5; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 4; > #BOTTOM RADII COMPLEX EQ = 1 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 4 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 4; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 4 > display_poles(); > fi;# end if 4 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y_higher[1, n]) = 0. or omniabs(array_y_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y_higher[1, n]*glob_h/array_y_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y_higher[1, m]) = 0. or omniabs(array_y_higher[1, m - 1]) = 0. or omniabs(array_y_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 4 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y[iii]) > array_norms[iii]) then # if number 5 > array_norms[iii] := omniabs(array_y[iii]); > fi;# end if 5; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 4; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y[iii]) then array_norms[iii] := omniabs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre ln 1 LINEAR $eq_no = 1 > array_tmp3[1] := ln(array_tmp2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre ln 2 LINEAR $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp2[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp4[2] := array_tmp3[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre ln ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := - array_tmp2[2] * array_tmp3[2] * 1 / array_tmp2[1] / 2; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp4[3] := array_tmp3[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre ln ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := - array_tmp2[2] * array_tmp3[3] * 2 / array_tmp2[1] / 3; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp4[4] := array_tmp3[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre ln ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := - array_tmp2[2] * array_tmp3[4] * 3 / array_tmp2[1] / 4; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp4[5] := array_tmp3[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit ln LINEAR $eq_no = 1 > array_tmp3[kkk] := - array_tmp2[2] * array_tmp3[kkk - 1] * (kkk - 2)/ array_tmp2[1] / (kkk - 1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp4[kkk] := array_tmp3[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp4[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := ln(array_tmp2[1]); array_tmp4[1] := array_const_0D0[1] + array_tmp3[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/array_tmp2[1]; array_tmp4[2] := array_tmp3[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp3[3] := -1/2*array_tmp2[2]*array_tmp3[2]/array_tmp2[1]; array_tmp4[3] := array_tmp3[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp3[4] := -2/3*array_tmp2[2]*array_tmp3[3]/array_tmp2[1]; array_tmp4[4] := array_tmp3[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp3[5] := -3/4*array_tmp2[2]*array_tmp3[4]/array_tmp2[1]; array_tmp4[5] := array_tmp3[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp3[kkk] := -array_tmp2[2]*array_tmp3[kkk - 1]*(kkk - 2)/( array_tmp2[1]*(kkk - 1)); array_tmp4[kkk] := array_tmp3[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp4[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0); > end; exact_soln_y := proc(x) return 10.0*(0.1*x + 0.2)*ln(0.1*x + 0.2) - x - 2.0 end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 1; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/lin_lnpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 20.0;"); > omniout_str(ALWAYS,"x_end := 30.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(2 + 1),[]); > array_last_rel_error:= Array(0..(2 + 1),[]); > array_type_pole:= Array(0..(2 + 1),[]); > array_type_real_pole:= Array(0..(2 + 1),[]); > array_type_complex_pole:= Array(0..(2 + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_0D1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D1[1] := 0.1; > array_const_0D2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D2[1] := 0.2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 20.0; > x_end := 30.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 4 > glob_h := glob_max_h; > fi;# end if 4; > if (glob_display_interval < glob_h) then # if number 4 > glob_h := glob_display_interval; > fi;# end if 4; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > atomall(); > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 4 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 5 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 5; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 5 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 5; > if (opt_iter > 100) then # if number 5 > glob_h := glob_max_h; > found_h := false; > fi;# end if 5; > if (glob_display_interval < glob_h) then # if number 5 > glob_h := glob_display_interval; > fi;# end if 5; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 5 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 5; > #BEGIN SOLUTION CODE > if (found_h) then # if number 5 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 6 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 6; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > atomall(); > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T02:38:14-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"lin_ln") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"lin_ln diffeq.mxt") > ; > logitem_str(html_log_file,"lin_ln maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/lin_lnpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 20.0;"); omniout_str(ALWAYS, "x_end := 30.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 3, []); array_last_rel_error := Array(0 .. 3, []); array_type_pole := Array(0 .. 3, []); array_type_real_pole := Array(0 .. 3, []); array_type_complex_pole := Array(0 .. 3, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_given_rad_poles := Array(0 .. 3, 0 .. 4, []); array_given_ord_poles := Array(0 .. 3, 0 .. 4, []); array_real_poles := Array(0 .. 3, 0 .. 4, []); array_complex_poles := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 2 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_0D1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D1[term] := 0.; term := term + 1 end do; array_const_0D1[1] := 0.1; array_const_0D2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D2[term] := 0.; term := term + 1 end do; array_const_0D2[1] := 0.2; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 20.0; x_end := 30.0; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 20; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; atomall(); estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; atomall(); display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T02:38:14-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "lin_ln"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "lin_ln diffeq.mxt"); logitem_str(html_log_file, "lin_ln maple results") ; logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/lin_lnpostode.ode################# diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 20.0; x_end := 30.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) return(10.0* (0.1 * x + 0.2) * ln(0.1 * x + 0.2) - x - 2.0); end; #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 = 1.0000000000000000000000000000000e-10 range = 10 estimated_steps = 10000000 step_error = 1.0000000000000000000000000000000e-17 est_needed_step_err = 1.0000000000000000000000000000000e-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 = 4.2317462075127271754888336638873e-193 estimated_step_error = 4.2317462075127271754888336638873e-193 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8398767474631590651374829370465e-185 estimated_step_error = 2.8398767474631590651374829370465e-185 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9058089440118641300262641163535e-177 estimated_step_error = 1.9058089440118641300262641163535e-177 best_h = 8.000e-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 = 1.2789666246796438930785001761984e-169 estimated_step_error = 1.2789666246796438930785001761984e-169 best_h = 1.60000e-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 = 8.5829982826675660653657113497235e-162 estimated_step_error = 8.5829982826675660653657113497235e-162 best_h = 3.200000e-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 = 5.7599507052610292315640890925756e-154 estimated_step_error = 5.7599507052610292315640890925756e-154 best_h = 6.4000000e-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 = 3.8654348822759801253117650709981e-146 estimated_step_error = 3.8654348822759801253117650709981e-146 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 = 2.5940459444953215373498723535153e-138 estimated_step_error = 2.5940459444953215373498723535153e-138 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.7408300758970383280085650572094e-130 estimated_step_error = 1.7408300758970383280085650572094e-130 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 = 1.1682449945633084430380232741949e-122 estimated_step_error = 1.1682449945633084430380232741949e-122 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 = 7.8398749767675357910744632558446e-115 estimated_step_error = 7.8398749767675357910744632558446e-115 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 = 5.2611376670765013831649522855211e-107 estimated_step_error = 5.2611376670765013831649522855211e-107 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 = 3.5305375706185376552541018751074e-99 estimated_step_error = 3.5305375706185376552541018751074e-99 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 = 2.3690994692900617090833537567727e-91 estimated_step_error = 2.3690994692900617090833537567727e-91 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5896017562085845425576235979981e-83 estimated_step_error = 1.5896017562085845425576235979981e-83 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 = 1.0663961355522221857153611828154e-75 estimated_step_error = 1.0663961355522221857153611828154e-75 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 = 7.1515353378326243150806186443036e-68 estimated_step_error = 7.1515353378326243150806186443036e-68 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 = 4.7927136443200482826630617622783e-60 estimated_step_error = 4.7927136443200482826630617622783e-60 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 20 y[1] (analytic) = -4.653938071986056271853946615743 y[1] (numeric) = -4.653938071986056271853946615743 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.01 y[1] (analytic) = -4.646051225999415219345774709019 y[1] (numeric) = -4.6460512259994152193457747090191 absolute error = 1e-31 relative error = 2.1523654203465854471529329129402e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.02 y[1] (analytic) = -4.638159836623249387277872764637 y[1] (numeric) = -4.6381598366232493872778727646371 absolute error = 1e-31 relative error = 2.1560274661169001599686090232265e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.03 y[1] (analytic) = -4.630263905920860245762876704971 y[1] (numeric) = -4.6302639059208602457628767049709 absolute error = 1e-31 relative error = 2.1597041125912269875477318337151e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.04 y[1] (analytic) = -4.622363435953676090439722877789 y[1] (numeric) = -4.6223634359536760904397228777886 absolute error = 4e-31 relative error = 8.6535817778567396360068251710812e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.05 y[1] (analytic) = -4.614458428781254592167020495606 y[1] (numeric) = -4.6144584287812545921670204956053 absolute error = 7e-31 relative error = 1.5169710829638574815761474036165e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.06 y[1] (analytic) = -4.606548886461285342091129181895 y[1] (numeric) = -4.6065488864612853420911291818945 absolute error = 5e-31 relative error = 1.0854112532475392249068921784698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.07 y[1] (analytic) = -4.598634811049592392099425068955 y[1] (numeric) = -4.5986348110495923920994250689543 absolute error = 7e-31 relative error = 1.5221908865605964536555402148582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=4000064, alloc=3079628, time=0.15 x[1] = 20.08 y[1] (analytic) = -4.590716204600136790669210391691 y[1] (numeric) = -4.5907162046001367906692103916908 absolute error = 2e-31 relative error = 4.3566186861995429163529043358989e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.09 y[1] (analytic) = -4.582793069165019114122693111398 y[1] (numeric) = -4.5827930691650191141226931113979 absolute error = 1e-31 relative error = 2.1820753957415736528089351797960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.1 y[1] (analytic) = -4.574865406794481993298434783459 y[1] (numeric) = -4.574865406794481993298434783459 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.14 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.11 y[1] (analytic) = -4.566933219536912635649636652446 y[1] (numeric) = -4.5669332195369126356496366524457 absolute error = 3e-31 relative error = 6.5689596405007214461619365268920e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.12 y[1] (analytic) = -4.558996509438845342779605817013 y[1] (numeric) = -4.5589965094388453427796058170125 absolute error = 5e-31 relative error = 1.0967325791208900474677094887384e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.13 y[1] (analytic) = -4.551055278544964023424715254968 y[1] (numeric) = -4.5510552785449640234247152549675 absolute error = 5e-31 relative error = 1.0986462905804497013988234150719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 18.79 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.14 y[1] (analytic) = -4.543109528898104701895143535609 y[1] (numeric) = -4.5431095288981047018951435356089 absolute error = 1e-31 relative error = 2.2011355738600079358702315391234e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.15 y[1] (analytic) = -4.535159262539258021983652171543 y[1] (numeric) = -4.5351592625392580219836521715429 absolute error = 1e-31 relative error = 2.2049942286703622215068864423500e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.16 y[1] (analytic) = -4.527204481507571746352630775412 y[1] (numeric) = -4.5272044815075717463526307754114 absolute error = 6e-31 relative error = 1.3253211831955916489488203991597e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.17 y[1] (analytic) = -4.519245187840353251409612487949 y[1] (numeric) = -4.519245187840353251409612487949 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.18 y[1] (analytic) = -4.511281383573072017681434532236 y[1] (numeric) = -4.5112813835730720176814345322353 absolute error = 7e-31 relative error = 1.5516655701169735439147739242879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.19 y[1] (analytic) = -4.503313070739362115697191224598 y[1] (numeric) = -4.5033130707393621156971912245977 absolute error = 3e-31 relative error = 6.6617620247029695261991652248920e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.2 y[1] (analytic) = -4.495340251371024687390099335036 y[1] (numeric) = -4.495340251371024687390099335036 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 15.92 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.21 y[1] (analytic) = -4.487362927498030423028368338973 y[1] (numeric) = -4.4873629274980304230283683389727 absolute error = 3e-31 relative error = 6.6854409783000925972230853185478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.22 y[1] (analytic) = -4.479381101148522033685140837267 y[1] (numeric) = -4.4793811011485220336851408372672 absolute error = 2e-31 relative error = 4.4649025274656717797351962872381e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.23 y[1] (analytic) = -4.471394774348816719257541242461 y[1] (numeric) = -4.4713947743488167192575412424607 absolute error = 3e-31 relative error = 6.7093158877632302845214919539363e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.471 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.24 y[1] (analytic) = -4.463403949123408632044843735829 y[1] (numeric) = -4.4634039491234086320448437358293 absolute error = 3e-31 relative error = 6.7213275656781765686416380055127e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.25 y[1] (analytic) = -4.455408627494971335895743491712 y[1] (numeric) = -4.4554086274949713358957434917118 absolute error = 2e-31 relative error = 4.4889260833623892562842296119384e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.05 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.26 y[1] (analytic) = -4.447408811484360260934688242435 y[1] (numeric) = -4.4474088114843602609346882424354 absolute error = 4e-31 relative error = 8.9940011578673969696212978572447e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.27 y[1] (analytic) = -4.439404503110615153877200418682 y[1] (numeric) = -4.4394045031106151538772004186825 absolute error = 5e-31 relative error = 1.1262771834593097172526944588427e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.28 y[1] (analytic) = -4.431395704390962523944093346025 y[1] (numeric) = -4.4313957043909625239440933460248 absolute error = 2e-31 relative error = 4.5132507530714273794373418807662e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 44.81 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.29 y[1] (analytic) = -4.423382417340818084384458308287 y[1] (numeric) = -4.423382417340818084384458308287 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 22.89 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.3 y[1] (analytic) = -4.415364643973789189617272702097 y[1] (numeric) = -4.4153646439737891896172727020966 absolute error = 4e-31 relative error = 9.0592744258604093954830603338859e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.31 y[1] (analytic) = -4.407342386301677268001453004124 y[1] (numeric) = -4.4073423863016772680014530041236 absolute error = 4e-31 relative error = 9.0757641440163002276010640933082e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.32 y[1] (analytic) = -4.399315646334480250244149852818 y[1] (numeric) = -4.3993156463344802502441498528185 absolute error = 5e-31 relative error = 1.1365404080896107812241301473863e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.33 y[1] (analytic) = -4.391284426080394993457056209616 y[1] (numeric) = -4.3912844260803949934570562096165 absolute error = 5e-31 relative error = 1.1386190268852470661583788864985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.34 y[1] (analytic) = -4.383248727545819700870473310299 y[1] (numeric) = -4.3832487275458197008704733102984 absolute error = 6e-31 relative error = 1.3688477138643690639646694263524e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.35 y[1] (analytic) = -4.375208552735356337214852945186 y[1] (numeric) = -4.3752085527353563372148529451858 absolute error = 2e-31 relative error = 4.5712106654884165321472811996926e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=8001508, alloc=4193536, time=0.30 TOP MAIN SOLVE Loop x[1] = 20.36 y[1] (analytic) = -4.367163903651813039779508516804 y[1] (numeric) = -4.3671639036518130397795085168038 absolute error = 2e-31 relative error = 4.5796311842740876118450726333566e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.37 y[1] (analytic) = -4.359114782296206525158161315281 y[1] (numeric) = -4.3591147822962065251581613152809 absolute error = 1e-31 relative error = 2.2940437449853985684144483117882e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.38 y[1] (analytic) = -4.351061190667764491690962524773 y[1] (numeric) = -4.3510611906677644916909625247728 absolute error = 2e-31 relative error = 4.5965798051510664282099775666385e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.39 y[1] (analytic) = -4.343003130763928017612605628314 y[1] (numeric) = -4.3430031307639280176126056283141 absolute error = 1e-31 relative error = 2.3025541771232880396345885559973e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.4 y[1] (analytic) = -4.334940604580353954916118113417 y[1] (numeric) = -4.3349406045803539549161181134164 absolute error = 6e-31 relative error = 1.3841020090702795071165682118845e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.41 y[1] (analytic) = -4.326873614110917318941895696169 y[1] (numeric) = -4.3268736141109173189418956961687 absolute error = 3e-31 relative error = 6.9334125919840108517158906174816e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.42 y[1] (analytic) = -4.318802161347713673701516677257 y[1] (numeric) = -4.3188021613477136737015166772566 absolute error = 4e-31 relative error = 9.2618273552770726200225699097501e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.43 y[1] (analytic) = -4.310726248281061512945848518924 y[1] (numeric) = -4.3107262482810615129458485189234 absolute error = 6e-31 relative error = 1.3918768333740864797725848424149e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.44 y[1] (analytic) = -4.302645876899504636986933287157 y[1] (numeric) = -4.3026458768995046369869332871563 absolute error = 7e-31 relative error = 1.6269059086601415187483029940019e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.45 y[1] (analytic) = -4.294561049189814525283113238018 y[1] (numeric) = -4.2945610491898145252831132380177 absolute error = 3e-31 relative error = 6.9855800526248463719263406364915e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.46 y[1] (analytic) = -4.286471767136992704796832540766 y[1] (numeric) = -4.2864717671369927047968325407656 absolute error = 4e-31 relative error = 9.3316839986366408204823817728568e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.47 y[1] (analytic) = -4.278378032724273114134525922943 y[1] (numeric) = -4.2783780327242731141345259229424 absolute error = 6e-31 relative error = 1.4024006186707811089123336233214e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.48 y[1] (analytic) = -4.270279847933124463477979893672 y[1] (numeric) = -4.2702798479331244634779798936714 absolute error = 6e-31 relative error = 1.4050601397714214046734574495925e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.49 y[1] (analytic) = -4.262177214743252590316527150712 y[1] (numeric) = -4.262177214743252590316527150712 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.5 y[1] (analytic) = -4.254070135132602810989409804104 y[1] (numeric) = -4.2540701351326028109894098041041 absolute error = 1e-31 relative error = 2.3506899703919178338044535297333e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.51 y[1] (analytic) = -4.245958611077362268047622154207 y[1] (numeric) = -4.2459586110773622680476221542073 absolute error = 3e-31 relative error = 7.0655422598167652336058660261989e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 68.24 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.52 y[1] (analytic) = -4.237842644551962273444518944328 y[1] (numeric) = -4.2378426445519622734445189443276 absolute error = 4e-31 relative error = 9.4387648044041339634159819078791e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.53 y[1] (analytic) = -4.22972223752908064756445026766 y[1] (numeric) = -4.2297222375290806475644502676594 absolute error = 6e-31 relative error = 1.4185328641119186838140860471647e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.54 y[1] (analytic) = -4.221597391979644054098659644669 y[1] (numeric) = -4.2215973919796440540986596446688 absolute error = 2e-31 relative error = 4.7375431958520683994680722031347e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.55 y[1] (analytic) = -4.21346810987283033077765720004 y[1] (numeric) = -4.2134681098728303307776572000393 absolute error = 7e-31 relative error = 1.6613392619723119168003172609308e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.56 y[1] (analytic) = -4.20533439317607081596925535762 y[1] (numeric) = -4.2053343931760708159692553576193 absolute error = 7e-31 relative error = 1.6645525291303323183727460339879e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.57 y[1] (analytic) = -4.197196243855052671151430037182 y[1] (numeric) = -4.1971962438550526711514300371822 absolute error = 2e-31 relative error = 4.7650857472488213850593802843118e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.58 y[1] (analytic) = -4.189053663873721199269145977963 y[1] (numeric) = -4.1890536638737211992691459779628 absolute error = 2e-31 relative error = 4.7743480042949621521616568405374e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 62.34 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.59 y[1] (analytic) = -4.180906655194282158984260530603 y[1] (numeric) = -4.180906655194282158984260530603 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.6 y[1] (analytic) = -4.172755219777204074827596051056 y[1] (numeric) = -4.1727552197772040748275960510562 absolute error = 2e-31 relative error = 4.7929962211078032100405709915310e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.61 y[1] (analytic) = -4.164599359581220543262246896894 y[1] (numeric) = -4.1645993595812205432622468968942 absolute error = 2e-31 relative error = 4.8023827199577582479652215804052e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.62 y[1] (analytic) = -4.156439076563332534667162968076 y[1] (numeric) = -4.1564390765633325346671629680754 absolute error = 6e-31 relative error = 1.4435433527299474999461544349639e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.63 y[1] (analytic) = -4.148274372678810691250027750294 y[1] (numeric) = -4.1482743726788106912500277502936 absolute error = 4e-31 relative error = 9.6425637280519121482880151483765e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=12002404, alloc=4259060, time=0.46 x[1] = 20.64 y[1] (analytic) = -4.140105249881197620898424909281 y[1] (numeric) = -4.1401052498811976208984249092806 absolute error = 4e-31 relative error = 9.6615901253109011885123500348928e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.65 y[1] (analytic) = -4.131931710122310186978263648611 y[1] (numeric) = -4.1319317101223101869782636486107 absolute error = 3e-31 relative error = 7.2605265780425891009411087750212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.66 y[1] (analytic) = -4.1237537553522417940884092814 y[1] (numeric) = -4.1237537553522417940884092813999 absolute error = 1e-31 relative error = 2.4249750574997227095890584320366e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.26 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.67 y[1] (analytic) = -4.115571387519364669780441777537 y[1] (numeric) = -4.115571387519364669780441777537 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.68 y[1] (analytic) = -4.107384608570332142252441432478 y[1] (numeric) = -4.1073846085703321422524414324783 absolute error = 3e-31 relative error = 7.3039179085890806484607681366679e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.69 y[1] (analytic) = -4.099193420450080914025677260917 y[1] (numeric) = -4.0991934204500809140256772609171 absolute error = 1e-31 relative error = 2.4395043059231944396077102515085e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.7 y[1] (analytic) = -4.09099782510183333161305024855 y[1] (numeric) = -4.0909978251018333316130502485497 absolute error = 3e-31 relative error = 7.3331742725268348028343149546181e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.71 y[1] (analytic) = -4.082797824467099651188120197447 y[1] (numeric) = -4.0827978244670996511881201974464 absolute error = 6e-31 relative error = 1.4695804832763522774104297024310e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.72 y[1] (analytic) = -4.074593420485680300263521574941 y[1] (numeric) = -4.0745934204856803002635215749412 absolute error = 2e-31 relative error = 4.9084651978886411564608080373936e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.73 y[1] (analytic) = -4.066384615095668135387550522224 y[1] (numeric) = -4.0663846150956681353875505222242 absolute error = 2e-31 relative error = 4.9183739102675776621946335778848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.74 y[1] (analytic) = -4.058171410233450695867681996707 y[1] (numeric) = -4.0581714102334506958676819967066 absolute error = 4e-31 relative error = 9.8566561035673347207612826490597e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.75 y[1] (analytic) = -4.049953807833712453529752911473 y[1] (numeric) = -4.0499538078337124535297529114729 absolute error = 1e-31 relative error = 2.4691639644524536309184361229000e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.34 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.76 y[1] (analytic) = -4.041731809829437058521524095489 y[1] (numeric) = -4.0417318098294370585215240954891 absolute error = 1e-31 relative error = 2.4741869254363031573265130626662e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.77 y[1] (analytic) = -4.033505418151909581169310929453 y[1] (numeric) = -4.0335054181519095811693109294528 absolute error = 2e-31 relative error = 4.9584661297328054034090491409196e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.92 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.78 y[1] (analytic) = -4.025274634730718749896349613997 y[1] (numeric) = -4.0252746347307187498963496139966 absolute error = 4e-31 relative error = 9.9372101607362510743632165308322e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.79 y[1] (analytic) = -4.017039461493759185211543199146 y[1] (numeric) = -4.0170394614937591852115431991457 absolute error = 3e-31 relative error = 7.4681865307950765743166797131220e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.8 y[1] (analytic) = -4.008799900367233629777208746238 y[1] (numeric) = -4.0087999003672336297772087462373 absolute error = 7e-31 relative error = 1.7461584948050791654096837000954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.81 y[1] (analytic) = -4.000555953275655174564424305684 y[1] (numeric) = -4.0005559532756551745644243056842 absolute error = 2e-31 relative error = 4.9993051549807721598945847671306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.82 y[1] (analytic) = -3.992307622141849481104551775767 y[1] (numeric) = -3.9923076221418494811045517757669 absolute error = 1e-31 relative error = 2.5048169997068159314126440186116e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 24.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.83 y[1] (analytic) = -3.984054908886956999845489158821 y[1] (numeric) = -3.9840549088869569998454891588206 absolute error = 4e-31 relative error = 1.0040022267457899195016224005738e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.84 y[1] (analytic) = -3.975797815430435184621183251502 y[1] (numeric) = -3.9757978154304351846211832515018 absolute error = 2e-31 relative error = 5.0304368905224932742971336451647e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.85 y[1] (analytic) = -3.967536343690060703242911395038 y[1] (numeric) = -3.9675363436900607032429113950375 absolute error = 5e-31 relative error = 1.2602279013655316750144165811827e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.86 y[1] (analytic) = -3.959270495581931644220818569227 y[1] (numeric) = -3.9592704955819316442208185692273 absolute error = 3e-31 relative error = 7.5771534259850095562372368021912e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.87 y[1] (analytic) = -3.951000273020469719624173840255 y[1] (numeric) = -3.9510002730204697196241738402552 absolute error = 2e-31 relative error = 5.0620092680252725686279782298036e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.88 y[1] (analytic) = -3.942725677918422464088787966826 y[1] (numeric) = -3.9427256779184224640887879668257 absolute error = 3e-31 relative error = 7.6089493540008642059962760363700e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.019 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.89 y[1] (analytic) = -3.934446712186865429980011831536 y[1] (numeric) = -3.9344467121868654299800118315356 absolute error = 4e-31 relative error = 1.0166613739131564924393995524003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 25.36 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.9 y[1] (analytic) = -3.926163377735204378719713294487 y[1] (numeric) = -3.9261633777352043787197132944871 absolute error = 1e-31 relative error = 2.5470157601460971654497887545506e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 80.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 20.91 y[1] (analytic) = -3.917875676471177468285608063706 y[1] (numeric) = -3.9178756764711774682856080637058 absolute error = 2e-31 relative error = 5.1048072097106355099263807382244e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 45.51 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop bytes used=16003644, alloc=4324584, time=0.62 x[1] = 20.92 y[1] (analytic) = -3.909583610300857436891298241712 y[1] (numeric) = -3.9095836103008574368912982417115 absolute error = 5e-31 relative error = 1.2789085740041842574654122584955e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.93 y[1] (analytic) = -3.901287181128653782855350339367 y[1] (numeric) = -3.9012871811286537828553503393668 absolute error = 2e-31 relative error = 5.1265131407767683359328182667083e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.94 y[1] (analytic) = -3.892986390857314940667722746664 y[1] (numeric) = -3.8929863908573149406677227466642 absolute error = 2e-31 relative error = 5.1374441089673556265725629104431e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.95 y[1] (analytic) = -3.884681241387930453261830915173 y[1] (numeric) = -3.8846812413879304532618309151732 absolute error = 2e-31 relative error = 5.1484275690157632059793522485482e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.96 y[1] (analytic) = -3.876371734619933140500516838226 y[1] (numeric) = -3.8763717346199331405005168382254 absolute error = 6e-31 relative error = 1.5478391678522241550540787369176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.97 y[1] (analytic) = -3.868057872451101263884167812333 y[1] (numeric) = -3.868057872451101263884167812333 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.98 y[1] (analytic) = -3.859739656777560687489207926588 y[1] (numeric) = -3.8597396567775606874892079265877 absolute error = 3e-31 relative error = 7.7725449558031990229718460909478e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 20.99 y[1] (analytic) = -3.851417089493787035145164255642 y[1] (numeric) = -3.8514170894937870351451642556421 absolute error = 1e-31 relative error = 2.5964469097046965350225909768858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21 y[1] (analytic) = -3.843090172492607843858488326106 y[1] (numeric) = -3.8430901724926078438584883261058 absolute error = 2e-31 relative error = 5.2041453888208161358975480698492e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.01 y[1] (analytic) = -3.834758907665204713491292085566 y[1] (numeric) = -3.8347589076652047134912920855661 absolute error = 1e-31 relative error = 2.6077258677230652981171750375043e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.02 y[1] (analytic) = -3.826423296901115452703136327745 y[1] (numeric) = -3.8264232969011154527031363277448 absolute error = 2e-31 relative error = 5.2268132530442439082642161234772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.84 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.03 y[1] (analytic) = -3.818083342088236221163988316297 y[1] (numeric) = -3.8180833420882362211639883162967 absolute error = 3e-31 relative error = 7.8573455087525686399560625564320e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.83 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.04 y[1] (analytic) = -3.809739045112823668046444203222 y[1] (numeric) = -3.8097390451128236680464442032222 absolute error = 2e-31 relative error = 5.2497033952118652806038386890559e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.05 y[1] (analytic) = -3.801390407859497066805290755582 y[1] (numeric) = -3.8013904078594970668052907555824 absolute error = 4e-31 relative error = 1.0522465652909186087648570181968e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.06 y[1] (analytic) = -3.793037432211240446252459885941 y[1] (numeric) = -3.7930374322112404462524598859414 absolute error = 4e-31 relative error = 1.0545638084220291634884232127156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.07 y[1] (analytic) = -3.784680120049404717935408527503 y[1] (numeric) = -3.784680120049404717935408527503 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.75 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.08 y[1] (analytic) = -3.776318473253709799826935504028 y[1] (numeric) = -3.7763184732537097998269355040285 absolute error = 5e-31 relative error = 1.3240408708675344436950819840877e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.09 y[1] (analytic) = -3.767952493702246736334426217108 y[1] (numeric) = -3.7679524937022467363344262171078 absolute error = 2e-31 relative error = 5.3079225477040877102584243365837e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.32 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.1 y[1] (analytic) = -3.759582183271479814636495208975 y[1] (numeric) = -3.7595821832714798146364952089753 absolute error = 3e-31 relative error = 7.9796101102636002481539940601930e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.11 y[1] (analytic) = -3.751207543836248677354975957611 y[1] (numeric) = -3.7512075438362486773549759576109 absolute error = 1e-31 relative error = 2.6658082452492875521039369787533e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.12 y[1] (analytic) = -3.742828577269770431570186622115 y[1] (numeric) = -3.7428285772697704315701866221149 absolute error = 1e-31 relative error = 2.6717761162587259480727124935331e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.13 y[1] (analytic) = -3.734445285443641754187379880084 y[1] (numeric) = -3.7344452854436417541873798800841 absolute error = 1e-31 relative error = 2.6777738688470375335831365285248e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.9 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.14 y[1] (analytic) = -3.726057670227840993662264484725 y[1] (numeric) = -3.7260576702278409936622644847245 absolute error = 5e-31 relative error = 1.3419008621233336880096035338732e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.15 y[1] (analytic) = -3.717665733490730268093465717504 y[1] (numeric) = -3.7176657334907302680934657175036 absolute error = 4e-31 relative error = 1.0759439623540790591299879509593e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.16 y[1] (analytic) = -3.70926947709905755968977152205 y[1] (numeric) = -3.7092694770990575596897715220494 absolute error = 6e-31 relative error = 1.6175691836475777152166437427706e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.17 y[1] (analytic) = -3.700868902917958805619990776541 y[1] (numeric) = -3.7008689029179588056199907765409 absolute error = 1e-31 relative error = 2.7020681527290730131939716344412e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.18 y[1] (analytic) = -3.692464012810959985253229894784 y[1] (numeric) = -3.6924640128109599852532298947839 absolute error = 1e-31 relative error = 2.7082186760128518274745194434153e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.19 y[1] (analytic) = -3.684054808639979203797373740321 y[1] (numeric) = -3.6840548086399792037973737403209 absolute error = 1e-31 relative error = 2.7144004417490306149924726711688e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.2 y[1] (analytic) = -3.675641292265328772343536693069 y[1] (numeric) = -3.675641292265328772343536693069 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 22.91 Order of pole (six term test) = -0.5 bytes used=20004700, alloc=4324584, time=0.78 TOP MAIN SOLVE Loop x[1] = 21.21 y[1] (analytic) = -3.667223465545717284324229623908 y[1] (numeric) = -3.6672234655457172843242296239077 absolute error = 3e-31 relative error = 8.1805759266801916367766035842925e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.51 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.22 y[1] (analytic) = -3.65880133033825168839296850914 y[1] (numeric) = -3.6588013303382516883929685091402 absolute error = 2e-31 relative error = 5.4662711074697856220262834540661e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.23 y[1] (analytic) = -3.650374888498439357733030453614 y[1] (numeric) = -3.6503748884984393577330304536137 absolute error = 3e-31 relative error = 8.2183339838666068775142173852405e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.24 y[1] (analytic) = -3.641944141880190155803042988307 y[1] (numeric) = -3.6419441418801901558030429883068 absolute error = 2e-31 relative error = 5.4915724187012927657035186515885e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 70.12 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.25 y[1] (analytic) = -3.633509092335818498527072665158 y[1] (numeric) = -3.6335090923358184985270726651581 absolute error = 1e-31 relative error = 2.7521604448694120982533525149087e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.26 y[1] (analytic) = -3.625069741716045412936859188623 y[1] (numeric) = -3.6250697417160454129368591886228 absolute error = 2e-31 relative error = 5.5171352346265055270541809817073e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.27 y[1] (analytic) = -3.616626091870000592273821599692 y[1] (numeric) = -3.6166260918700005922738215996924 absolute error = 4e-31 relative error = 1.1060031914805363185539205587800e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.28 y[1] (analytic) = -3.608178144645224447558443363692 y[1] (numeric) = -3.6081781446452244475584433636922 absolute error = 2e-31 relative error = 5.5429635672732306186458490051899e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 23.17 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.29 y[1] (analytic) = -3.59972590188767015563462360788 y[1] (numeric) = -3.5997259018876701556346236078802 absolute error = 2e-31 relative error = 5.5559785786779335203506440214394e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.3 y[1] (analytic) = -3.591269365441705703696562208506 y[1] (numeric) = -3.5912693654417057036965622085061 absolute error = 1e-31 relative error = 2.7845307556789343990347313159994e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.31 y[1] (analytic) = -3.582808537150115930305726939346 y[1] (numeric) = -3.5828085371501159303057269393457 absolute error = 3e-31 relative error = 8.3733193356357773405026649490221e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.32 y[1] (analytic) = -3.574343418854104562905431464604 y[1] (numeric) = -3.5743434188541045629054314646041 absolute error = 1e-31 relative error = 2.7977166232129677995024227538237e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.33 y[1] (analytic) = -3.565874012393296251840533588282 y[1] (numeric) = -3.5658740123932962518405335882822 absolute error = 2e-31 relative error = 5.6087231154239978294253827418643e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.34 y[1] (analytic) = -3.557400319605738600889743859419 y[1] (numeric) = -3.5574003196057386008897438594185 absolute error = 5e-31 relative error = 1.4055207597648562029767294820780e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.35 y[1] (analytic) = -3.548922342327904194318015377863 y[1] (numeric) = -3.5489223423279041943180153778629 absolute error = 1e-31 relative error = 2.8177567823139607410747950540521e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.36 y[1] (analytic) = -3.540440082394692620456466448201 y[1] (numeric) = -3.5404400823946926204564664482007 absolute error = 3e-31 relative error = 8.4735228677301939592146379405798e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.46 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.37 y[1] (analytic) = -3.531953541639432491817268589938 y[1] (numeric) = -3.5319535416394324918172685899378 absolute error = 2e-31 relative error = 5.6625886394634081728799716892687e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.38 y[1] (analytic) = -3.523462721893883461750913329875 y[1] (numeric) = -3.5234627218938834617509133298745 absolute error = 5e-31 relative error = 1.4190585780662008615617351623465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.39 y[1] (analytic) = -3.514967624988238237653252177547 y[1] (numeric) = -3.514967624988238237653252177547 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.76 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.4 y[1] (analytic) = -3.506468252751124590729685216504 y[1] (numeric) = -3.5064682527511245907296852165041 absolute error = 1e-31 relative error = 2.8518723910174129583089568739515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.41 y[1] (analytic) = -3.497964607009607362323854832815 y[1] (numeric) = -3.4979646070096073623238548328146 absolute error = 4e-31 relative error = 1.1435221477039415248725115505375e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 103.3 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.42 y[1] (analytic) = -3.489456689589190466818182247381 y[1] (numeric) = -3.4894566895891904668181822473807 absolute error = 3e-31 relative error = 8.5973269390347022379682586516814e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.43 y[1] (analytic) = -3.480944502313818891113565720166 y[1] (numeric) = -3.4809445023138188911135657201657 absolute error = 3e-31 relative error = 8.6183505597571859202565997983447e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.804 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.44 y[1] (analytic) = -3.47242804700588069069554055214 y[1] (numeric) = -3.4724280470058806906955405521404 absolute error = 4e-31 relative error = 1.1519317163242650902001293032198e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.45 y[1] (analytic) = -3.463907325486208982294182324419 y[1] (numeric) = -3.4639073254862089822941823244189 absolute error = 1e-31 relative error = 2.8869132630724630718548339579132e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.46 y[1] (analytic) = -3.455382339574083933145016183504 y[1] (numeric) = -3.4553823395740839331450161835034 absolute error = 6e-31 relative error = 1.7364214464149775659441812403505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.47 y[1] (analytic) = -3.446853091087234746858176406594 y[1] (numeric) = -3.4468530910872347468581764065936 absolute error = 4e-31 relative error = 1.1604788177201619887959146640953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.48 y[1] (analytic) = -3.438319581841841645903041961355 y[1] (numeric) = -3.4383195818418416459030419613546 absolute error = 4e-31 relative error = 1.1633589911549981520202306990261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=24005968, alloc=4390108, time=0.94 x[1] = 21.49 y[1] (analytic) = -3.429781813652537850715555310185 y[1] (numeric) = -3.4297818136525378507155553101852 absolute error = 2e-31 relative error = 5.8312747243536895285409518851278e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 22.69 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.5 y[1] (analytic) = -3.421239788332411555435413299704 y[1] (numeric) = -3.4212397883324115554354132997035 absolute error = 5e-31 relative error = 1.4614585090035771277595702258953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.51 y[1] (analytic) = -3.412693507693007900280300621674 y[1] (numeric) = -3.4126935076930079002803006216737 absolute error = 3e-31 relative error = 8.7907103091364624871051884220013e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.52 y[1] (analytic) = -3.404142973544330940564318031758 y[1] (numeric) = -3.4041429735443309405643180317584 absolute error = 4e-31 relative error = 1.1750387780673247406330562985339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.88 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.53 y[1] (analytic) = -3.395588187694845612367739267103 y[1] (numeric) = -3.3955881876948456123677392671025 absolute error = 5e-31 relative error = 1.4724989379216616333955273399133e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.54 y[1] (analytic) = -3.387029151951479694865212412657 y[1] (numeric) = -3.3870291519514796948652124126571 absolute error = 1e-31 relative error = 2.9524398968454031436358477935085e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 51.66 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.55 y[1] (analytic) = -3.378465868119625769319503329146 y[1] (numeric) = -3.3784658681196257693195033291462 absolute error = 2e-31 relative error = 5.9198466939467786225931758430450e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.56 y[1] (analytic) = -3.369898338003143174747860672486 y[1] (numeric) = -3.3698983380031431747478606724857 absolute error = 3e-31 relative error = 8.9023457063030304304032160485938e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.57 y[1] (analytic) = -3.361326563404359960268064005098 y[1] (numeric) = -3.3613265634043599602680640050984 absolute error = 4e-31 relative error = 1.1900063634247991614038260513443e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.58 y[1] (analytic) = -3.352750546124074834131198523744 y[1] (numeric) = -3.3527505461240748341311985237443 absolute error = 3e-31 relative error = 8.9478771496081932565095828587742e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.59 y[1] (analytic) = -3.344170287961559109448182006031 y[1] (numeric) = -3.3441702879615591094481820060313 absolute error = 3e-31 relative error = 8.9708350403072676566830574742432e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.6 y[1] (analytic) = -3.335585790714558646617051708491 y[1] (numeric) = -3.3355857907145586466170517084911 absolute error = 1e-31 relative error = 2.9979741572942039795567535095387e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.61 y[1] (analytic) = -3.326997056179295792458001132836 y[1] (numeric) = -3.3269970561792957924580011328355 absolute error = 5e-31 relative error = 1.5028567550768954173512884283506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.62 y[1] (analytic) = -3.318404086150471316063138813554 y[1] (numeric) = -3.3184040861504713160631388135534 absolute error = 6e-31 relative error = 1.8080980628734475060275165192260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.63 y[1] (analytic) = -3.309806882421266341367923569203 y[1] (numeric) = -3.3098068824212663413679235692034 absolute error = 4e-31 relative error = 1.2085297245722770554366901231990e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.64 y[1] (analytic) = -3.301205446783344276451213001415 y[1] (numeric) = -3.3012054467833442764512130014146 absolute error = 4e-31 relative error = 1.2116786017960660126648304429685e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.65 y[1] (analytic) = -3.292599781026852739570844419552 y[1] (numeric) = -3.2925997810268527395708444195516 absolute error = 4e-31 relative error = 1.2148454917143111084936870351070e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.66 y[1] (analytic) = -3.283989886940425481941649815059 y[1] (numeric) = -3.2839898869404254819416498150591 absolute error = 1e-31 relative error = 3.0450763687694050919957380279166e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.53 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.67 y[1] (analytic) = -3.27537576631118430726278900749 y[1] (numeric) = -3.2753757663111843072627890074902 absolute error = 2e-31 relative error = 6.1061696205087742706993240411653e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.68 y[1] (analytic) = -3.266757420924740988001267633975 y[1] (numeric) = -3.2667574209247409880012676339748 absolute error = 2e-31 relative error = 6.1222788909555695658474823413270e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.69 y[1] (analytic) = -3.258134852565199178438489255218 y[1] (numeric) = -3.2581348525651991784384892552182 absolute error = 2e-31 relative error = 6.1384813413274078285516444777601e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.7 y[1] (analytic) = -3.249508063015156324486673503866 y[1] (numeric) = -3.2495080630151563244866735038656 absolute error = 4e-31 relative error = 1.2309555546350842331131269172413e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 24.6 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.71 y[1] (analytic) = -3.240877054055705570281954905049 y[1] (numeric) = -3.2408770540557055702819549050494 absolute error = 4e-31 relative error = 1.2342337994569436395349254092277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.72 y[1] (analytic) = -3.232241827466437661560959753982 y[1] (numeric) = -3.232241827466437661560959753982 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.823 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.73 y[1] (analytic) = -3.223602385025442845827641241394 y[1] (numeric) = -3.2236023850254428458276412413936 absolute error = 4e-31 relative error = 1.2408478224799518195408824398390e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 25.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.74 y[1] (analytic) = -3.214958728509312769317135874271 y[1] (numeric) = -3.2149587285093127693171358742707 absolute error = 3e-31 relative error = 9.3313795085357653340794224415225e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 19.41 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.75 y[1] (analytic) = -3.206310859693142370763387146559 y[1] (numeric) = -3.2063108596931423707633871465586 absolute error = 4e-31 relative error = 1.2475396725515307852270391021220e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.76 y[1] (analytic) = -3.197658780350531771977265372074 y[1] (numeric) = -3.1976587803505317719772653720736 absolute error = 4e-31 relative error = 1.2509152085206272307028188073597e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=28007136, alloc=4390108, time=1.10 x[1] = 21.77 y[1] (analytic) = -3.189002492253588165241895599666 y[1] (numeric) = -3.1890024922535881652418955996664 absolute error = 4e-31 relative error = 1.2543107161930438675986327755401e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.78 y[1] (analytic) = -3.180341997172927697531888588511 y[1] (numeric) = -3.1803419971729276975318885885114 absolute error = 4e-31 relative error = 1.2577263714266212214736406171629e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.79 y[1] (analytic) = -3.171677296877677351563152929102 y[1] (numeric) = -3.171677296877677351563152929102 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.887 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.8 y[1] (analytic) = -3.163008393135476823679949552943 y[1] (numeric) = -3.1630083931354768236799495529432 absolute error = 2e-31 relative error = 6.3230941920372473962745051609465e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.81 y[1] (analytic) = -3.154335287712480398585833080878 y[1] (numeric) = -3.154335287712480398585833080878 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.82 y[1] (analytic) = -3.145657982373358820925107716304 y[1] (numeric) = -3.1456579823733588209251077163037 absolute error = 3e-31 relative error = 9.5369554376554893889864889481119e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.83 y[1] (analytic) = -3.136976478881301163721408695055 y[1] (numeric) = -3.1369764788813011637214086950547 absolute error = 3e-31 relative error = 9.5633487219191732945786487537870e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.84 y[1] (analytic) = -3.128290778998016693680003658292 y[1] (numeric) = -3.1282907789980166936800036582919 absolute error = 1e-31 relative error = 3.1966337870941056480327456094025e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.85 y[1] (analytic) = -3.119600884483736733360391718174 y[1] (numeric) = -3.1196008844837367333603917181743 absolute error = 3e-31 relative error = 9.6166147885179565092779636100764e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.86 y[1] (analytic) = -3.110906797097216520225761438238 y[1] (numeric) = -3.1109067970972165202257614382384 absolute error = 4e-31 relative error = 1.2857987271532516832375700372822e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.87 y[1] (analytic) = -3.102208518595737062575852451105 y[1] (numeric) = -3.102208518595737062575852451105 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.88 y[1] (analytic) = -3.093506050735106992369748985215 y[1] (numeric) = -3.0935060507351069923697489852148 absolute error = 2e-31 relative error = 6.4651562570072938531058972159755e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.89 y[1] (analytic) = -3.084799395269664414945117169599 y[1] (numeric) = -3.0847993952696644149451171695988 absolute error = 2e-31 relative error = 6.4834037606039068605444196019596e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.9 y[1] (analytic) = -3.076088553952278755640381631053 y[1] (numeric) = -3.0760885539522787556403816310531 absolute error = 1e-31 relative error = 3.2508817040236404456196044554816e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.91 y[1] (analytic) = -3.067373528534352603326320591356 y[1] (numeric) = -3.0673735285343526033263205913558 absolute error = 2e-31 relative error = 6.5202362261880662609127865841171e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.92 y[1] (analytic) = -3.058654320765823550853542413169 y[1] (numeric) = -3.058654320765823550853542413169 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.93 y[1] (analytic) = -3.049930932395166032422290331855 y[1] (numeric) = -3.049930932395166032422290331855 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.94 y[1] (analytic) = -3.041203365169393157881005946447 y[1] (numeric) = -3.0412033651693931578810059464469 absolute error = 1e-31 relative error = 3.2881720816598551104889613936713e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.95 y[1] (analytic) = -3.032471620834058543960065926284 y[1] (numeric) = -3.0324716208340585439600659262836 absolute error = 4e-31 relative error = 1.3190560374971720401338412410684e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.96 y[1] (analytic) = -3.023735701133258142447090320197 y[1] (numeric) = -3.0237357011332581424470903201966 absolute error = 4e-31 relative error = 1.3228669418761865551756821291672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.125 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 21.97 y[1] (analytic) = -3.014995607809632065310204832462 y[1] (numeric) = -3.0149956078096320653102048324619 absolute error = 1e-31 relative error = 3.3167544171863363086773087282711e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.98 y[1] (analytic) = -3.006251342604366406775623453846 y[1] (numeric) = -3.0062513426043664067756234538457 absolute error = 3e-31 relative error = 9.9792055224532531504877309877529e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 21.99 y[1] (analytic) = -2.997502907257195062365901906825 y[1] (numeric) = -2.9975029072571950623659019068252 absolute error = 2e-31 relative error = 6.6722203843667324463828305659484e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22 y[1] (analytic) = -2.988750303506401544905196481295 y[1] (numeric) = -2.9887503035064015449051964812955 absolute error = 5e-31 relative error = 1.6729400225017126792312695032144e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.01 y[1] (analytic) = -2.979993533088820797497847000632 y[1] (numeric) = -2.9799935330888207974978470006319 absolute error = 1e-31 relative error = 3.3557119802319862906033748055225e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.02 y[1] (analytic) = -2.9712325977398410034865868677 y[1] (numeric) = -2.9712325977398410034865868677002 absolute error = 2e-31 relative error = 6.7312131723425530565730912226166e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.03 y[1] (analytic) = -2.962467499193405393396667396155 y[1] (numeric) = -2.9624674991934053933966673961545 absolute error = 5e-31 relative error = 1.6877822292941124394679706455364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 6.348 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.04 y[1] (analytic) = -2.953698239182014048872167933964 y[1] (numeric) = -2.9536982391820140488721679339646 absolute error = 6e-31 relative error = 2.0313517204999306798409758607775e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.05 y[1] (analytic) = -2.944924819436725703610747633435 y[1] (numeric) = -2.9449248194367257036107476334349 absolute error = 1e-31 relative error = 3.3956724239611301844286444850924e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=32009432, alloc=4390108, time=1.26 TOP MAIN SOLVE Loop x[1] = 22.06 y[1] (analytic) = -2.936147241687159541303079114852 y[1] (numeric) = -2.9361472416871595413030791148524 absolute error = 4e-31 relative error = 1.3623294987418726275454116809260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.07 y[1] (analytic) = -2.927365507661496990583188709183 y[1] (numeric) = -2.9273655076614969905831887091835 absolute error = 5e-31 relative error = 1.7080203981750850242400159401076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.97 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.08 y[1] (analytic) = -2.91857961908648351699591244878 y[1] (numeric) = -2.9185796190864835169959124487801 absolute error = 1e-31 relative error = 3.4263242073656375492488449517565e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 18.15 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.09 y[1] (analytic) = -2.909789577687430411987661503701 y[1] (numeric) = -2.909789577687430411987661503701 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.1 y[1] (analytic) = -2.900995385188216578926675334856 y[1] (numeric) = -2.9009953851882165789266753348558 absolute error = 2e-31 relative error = 6.8941853896476984610832953860655e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.11 y[1] (analytic) = -2.892197043311290316158925453588 y[1] (numeric) = -2.8921970433112903161589254535883 absolute error = 3e-31 relative error = 1.0372737248100100260909317795069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.12 y[1] (analytic) = -2.883394553777671097105817340383 y[1] (numeric) = -2.8833945537776710971058173403826 absolute error = 4e-31 relative error = 1.3872537820949309497131593508076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.13 y[1] (analytic) = -2.874587918306951347409822782953 y[1] (numeric) = -2.8745879183069513474098227829532 absolute error = 2e-31 relative error = 6.9575189795480035739155030641784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.14 y[1] (analytic) = -2.865777138617298219134159645919 y[1] (numeric) = -2.8657771386172982191341596459195 absolute error = 5e-31 relative error = 1.7447274362766525987660085605805e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.15 y[1] (analytic) = -2.856962216425455362022620880422 y[1] (numeric) = -2.8569622164254553620226208804219 absolute error = 1e-31 relative error = 3.5002212988702725217034721630311e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.16 y[1] (analytic) = -2.84814315344674469182563942226 y[1] (numeric) = -2.8481431534467446918256394222598 absolute error = 2e-31 relative error = 7.0221189464428951880384591785623e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.17 y[1] (analytic) = -2.83931995139506815569866051128 y[1] (numeric) = -2.8393199513950681556986605112807 absolute error = 7e-31 relative error = 2.4653790766203111975743472713963e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.18 y[1] (analytic) = -2.830492611982909494678877892675 y[1] (numeric) = -2.8304926119829094946788778926751 absolute error = 1e-31 relative error = 3.5329539309394176818137546807960e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.19 y[1] (analytic) = -2.82166113692133600324637533239 y[1] (numeric) = -2.8216611369213360032463753323902 absolute error = 2e-31 relative error = 7.0880233413930215126030410055453e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.2 y[1] (analytic) = -2.812825527920000285975699893923 y[1] (numeric) = -2.8128255279200002859756998939234 absolute error = 4e-31 relative error = 1.4220576286357438816649327110110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.21 y[1] (analytic) = -2.803985786687142011283878482147 y[1] (numeric) = -2.8039857866871420112838784821473 absolute error = 3e-31 relative error = 1.0699055659424169911018626363441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.22 y[1] (analytic) = -2.795141914929589662280874261414 y[1] (numeric) = -2.7951419149295896622808742614146 absolute error = 6e-31 relative error = 2.1465815270245917121025456540346e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.23 y[1] (analytic) = -2.786293914352762284728464699841 y[1] (numeric) = -2.7862939143527622847284646998409 absolute error = 1e-31 relative error = 3.5889968206469467533945836318412e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.24 y[1] (analytic) = -2.777441786660671232113508179236 y[1] (numeric) = -2.7774417866606712321135081792359 absolute error = 1e-31 relative error = 3.6004354971641144034920821030364e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.25 y[1] (analytic) = -2.768585533555921907841551340496 y[1] (numeric) = -2.7685855335559219078415513404967 absolute error = 7e-31 relative error = 2.5283668917424865608510364816525e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 89.67 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.26 y[1] (analytic) = -2.759725156739715504556714607256 y[1] (numeric) = -2.7597251567397155045567146072568 absolute error = 8e-31 relative error = 2.8988393936485476437416595938398e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.27 y[1] (analytic) = -2.750860657911850740593778646055 y[1] (numeric) = -2.7508606579118507405937786460558 absolute error = 8e-31 relative error = 2.9081807459025261827604864780307e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.28 y[1] (analytic) = -2.741992038770725593568379879122 y[1] (numeric) = -2.7419920387707255935683798791227 absolute error = 7e-31 relative error = 2.5528885208354581952528587751328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 110.1 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.29 y[1] (analytic) = -2.733119301013339031111208565902 y[1] (numeric) = -2.7331193010133390311112085659026 absolute error = 6e-31 relative error = 2.1952938526230534665568980874177e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 26.97 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.3 y[1] (analytic) = -2.724242446335292738752088411573 y[1] (numeric) = -2.7242424463352927387520884115736 absolute error = 6e-31 relative error = 2.2024471456537666268257787847163e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.31 y[1] (analytic) = -2.71536147643079284495980214485 y[1] (numeric) = -2.7153614764307928449598021448502 absolute error = 2e-31 relative error = 7.3655018580763699764600224177911e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.32 y[1] (analytic) = -2.706476392992651643343513033219 y[1] (numeric) = -2.706476392992651643343513033219 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.33 y[1] (analytic) = -2.697587197712289312021617871263 y[1] (numeric) = -2.6975871977122893120216178712629 absolute error = 1e-31 relative error = 3.7070164065430696934504270581462e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.34 y[1] (analytic) = -2.688693892279735630163852586762 y[1] (numeric) = -2.6886938922797356301638525867622 bytes used=36011424, alloc=4390108, time=1.42 absolute error = 2e-31 relative error = 7.4385559685420562775730072095831e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.548 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.35 y[1] (analytic) = -2.679796478383631691712457259684 y[1] (numeric) = -2.6797964783836316917124572596847 absolute error = 7e-31 relative error = 2.6121386666729923302469231217285e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 66.68 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.36 y[1] (analytic) = -2.670894957711231616288193040846 y[1] (numeric) = -2.6708949577112316162881930408466 absolute error = 6e-31 relative error = 2.2464380273275802403383493071333e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.37 y[1] (analytic) = -2.661989331948404257286989189816 y[1] (numeric) = -2.6619893319484042572869891898166 absolute error = 6e-31 relative error = 2.2539534354964478879230089763192e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.38 y[1] (analytic) = -2.653079602779634907172984225403 y[1] (numeric) = -2.6530796027796349071729842254034 absolute error = 4e-31 relative error = 1.5076818636761576481965078160850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.39 y[1] (analytic) = -2.644165771888026999973710996683 y[1] (numeric) = -2.6441657718880269999737109966835 absolute error = 5e-31 relative error = 1.8909555721348835190687018126898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.4 y[1] (analytic) = -2.635247840955303810983161337853 y[1] (numeric) = -2.6352478409553038109831613378533 absolute error = 3e-31 relative error = 1.1384128480729424932433388806243e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.41 y[1] (analytic) = -2.626325811661810153678451866098 y[1] (numeric) = -2.6263258116618101536784518660983 absolute error = 3e-31 relative error = 1.1422802101243284619243167813599e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.42 y[1] (analytic) = -2.617399685686514073855798418023 y[1] (numeric) = -2.6173996856865140738557984180237 absolute error = 7e-31 relative error = 2.6744100407286401380378134679435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.43 y[1] (analytic) = -2.608469464707008540991492596858 y[1] (numeric) = -2.6084694647070085409914925968587 absolute error = 7e-31 relative error = 2.6835660124494736691630061431584e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.44 y[1] (analytic) = -2.599535150399513136833559919494 y[1] (numeric) = -2.5995351503995131368335599194939 absolute error = 1e-31 relative error = 3.8468416164571332066455529616220e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.45 y[1] (analytic) = -2.59059674443887574122976510931 y[1] (numeric) = -2.59059674443887574122976510931 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.46 y[1] (analytic) = -2.581654248498574215197616177573 y[1] (numeric) = -2.5816542484985742151976161775732 absolute error = 2e-31 relative error = 7.7469707694713580129464125524831e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.47 y[1] (analytic) = -2.572707664250718081242005072777 y[1] (numeric) = -2.5727076642507180812420050727769 absolute error = 1e-31 relative error = 3.8869554201419248367383900823775e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 18.4 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.48 y[1] (analytic) = -2.563756993366050200926108853574 y[1] (numeric) = -2.5637569933660502009261088535743 absolute error = 3e-31 relative error = 1.1701577051814066127066480759439e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.49 y[1] (analytic) = -2.554802237513948449701161556738 y[1] (numeric) = -2.5548022375139484497011615567384 absolute error = 4e-31 relative error = 1.5656789168512544041405988359467e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 66.03 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.5 y[1] (analytic) = -2.545843398362427389000693186776 y[1] (numeric) = -2.5458433983624273890006931867767 absolute error = 7e-31 relative error = 2.7495799641496554112652536421153e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.51 y[1] (analytic) = -2.536880477578139935604818548292 y[1] (numeric) = -2.5368804775781399356048185482925 absolute error = 5e-31 relative error = 1.9709245446097261328316716796323e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 66.33 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.52 y[1] (analytic) = -2.527913476826379028280144975788 y[1] (numeric) = -2.5279134768263790282801449757884 absolute error = 4e-31 relative error = 1.5823326378328913549933924546699e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 25.91 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.53 y[1] (analytic) = -2.518942397771079291700854388229 y[1] (numeric) = -2.5189423977710792917008543882294 absolute error = 4e-31 relative error = 1.5879680311623857809431706917887e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.54 y[1] (analytic) = -2.50996724207481869765650150719 y[1] (numeric) = -2.5099672420748186976565015071901 absolute error = 1e-31 relative error = 3.9841157415798312035907559938987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.55 y[1] (analytic) = -2.50098801139882022355205652768 y[1] (numeric) = -2.5009880113988202235520565276804 absolute error = 4e-31 relative error = 1.5993679225046631891290189821670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.56 y[1] (analytic) = -2.492004707402953508205707019647 y[1] (numeric) = -2.4920047074029535082057070196477 absolute error = 7e-31 relative error = 2.8089834578583363250301379127497e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.521 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.57 y[1] (analytic) = -2.483017331745736504949920365566 y[1] (numeric) = -2.4830173317457365049499203655665 absolute error = 5e-31 relative error = 2.0136790573606858234502560307249e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 56.27 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.58 y[1] (analytic) = -2.474025886084337132041254605322 y[1] (numeric) = -2.4740258860843371320412546053223 absolute error = 3e-31 relative error = 1.2125984682998312503776179345261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.59 y[1] (analytic) = -2.465030372074574920384392163651 y[1] (numeric) = -2.4650303720745749203843921636511 absolute error = 1e-31 relative error = 4.0567451473565326738360030720945e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 79.37 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.6 y[1] (analytic) = -2.456030791370922658575857577585 y[1] (numeric) = -2.4560307913709226585758575775854 absolute error = 4e-31 relative error = 1.6286440764723698487544923778260e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.61 y[1] (analytic) = -2.447027145626508035272867021555 y[1] (numeric) = -2.447027145626508035272867021555 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.62 y[1] (analytic) = -2.438019436493115278892744145878 y[1] (numeric) = -2.4380194364931152788927441458779 absolute error = 1e-31 relative error = 4.1016900235972499359854388712135e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=40012868, alloc=4390108, time=1.58 TOP MAIN SOLVE Loop x[1] = 22.63 y[1] (analytic) = -2.429007665621186794648323500223 y[1] (numeric) = -2.4290076656211867946483235002234 absolute error = 4e-31 relative error = 1.6467630203946073417663266554819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 56.66 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.64 y[1] (analytic) = -2.41999183465982479892474960712 y[1] (numeric) = -2.4199918346598247989247496071202 absolute error = 2e-31 relative error = 8.2644906951974797815891550688485e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 26.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.65 y[1] (analytic) = -2.41097194525679295100306658159 y[1] (numeric) = -2.4109719452567929510030665815896 absolute error = 4e-31 relative error = 1.6590819349305864502597092705528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.76 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.66 y[1] (analytic) = -2.401947999058517982135980061388 y[1] (numeric) = -2.4019479990585179821359800613883 absolute error = 3e-31 relative error = 1.2489862399918308329372259393299e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.67 y[1] (analytic) = -2.392919997710091321981160118026 y[1] (numeric) = -2.3929199977100913219811601180257 absolute error = 3e-31 relative error = 1.2536984115101444562022610055476e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 62.91 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.68 y[1] (analytic) = -2.383887942855270722397440761555 y[1] (numeric) = -2.3838879428552707223974407615553 absolute error = 3e-31 relative error = 1.2584484136476604218503371755783e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.69 y[1] (analytic) = -2.374851836136481878609258632007 y[1] (numeric) = -2.3748518361364818786092586320074 absolute error = 4e-31 relative error = 1.6843156019818835731656264001244e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 26.85 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.7 y[1] (analytic) = -2.365811679194820047744660487114 y[1] (numeric) = -2.3658116791948200477446604871143 absolute error = 3e-31 relative error = 1.2680637374404286902366682679877e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.71 y[1] (analytic) = -2.356767473670051664752196149556 y[1] (numeric) = -2.3567674736700516647521961495563 absolute error = 3e-31 relative error = 1.2729299914039806251801422616146e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.72 y[1] (analytic) = -2.347719221200615955702000667208 y[1] (numeric) = -2.3477192212006159557020006672083 absolute error = 3e-31 relative error = 1.2778359409034483180581710072318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.73 y[1] (analytic) = -2.338666923423626548476356566678 y[1] (numeric) = -2.3386669234236265484763565666784 absolute error = 4e-31 relative error = 1.7103760950038627104989609112205e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.74 y[1] (analytic) = -2.329610581974873080855014243676 y[1] (numeric) = -2.3296105819748730808550142436759 absolute error = 1e-31 relative error = 4.2925629190449216809883145464806e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.837 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.75 y[1] (analytic) = -2.320550198488822806000535733316 y[1] (numeric) = -2.3205501984888228060005357333159 absolute error = 1e-31 relative error = 4.3093228521891706612548175123472e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.76 y[1] (analytic) = -2.311485774598622195348914339239 y[1] (numeric) = -2.3114857745986221953489143392386 absolute error = 4e-31 relative error = 1.7304886943094338329187616234905e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.77 y[1] (analytic) = -2.302417311936098538910709872281 y[1] (numeric) = -2.3024173119360985389107098722812 absolute error = 2e-31 relative error = 8.6865225935875353101563950755785e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.78 y[1] (analytic) = -2.293344812131761542987926557266 y[1] (numeric) = -2.2933448121317615429879265572658 absolute error = 2e-31 relative error = 8.7208865819916322847896619053223e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.79 y[1] (analytic) = -2.28426827681480492531184801015 y[1] (numeric) = -2.28426827681480492531184801015 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.8 y[1] (analytic) = -2.275187707613108007607031067206 y[1] (numeric) = -2.2751877076131080076070310672058 absolute error = 2e-31 relative error = 8.7904834986041370063838577599376e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 38.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.81 y[1] (analytic) = -2.266103106153237305586647662934 y[1] (numeric) = -2.2661031061532373055866476629338 absolute error = 2e-31 relative error = 8.8257237482677762469663008082693e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.82 y[1] (analytic) = -2.25701447406044811638435140397 y[1] (numeric) = -2.2570144740604481163843514039703 absolute error = 3e-31 relative error = 1.3291895264645312136387349931871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.83 y[1] (analytic) = -2.247921812958686103427832972187 y[1] (numeric) = -2.2479218129586861034278329721868 absolute error = 2e-31 relative error = 8.8971066007301447641115575422928e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.84 y[1] (analytic) = -2.238825124470588878759216011405 y[1] (numeric) = -2.2388251244705888787592160114049 absolute error = 1e-31 relative error = 4.4666284519942944525139214372327e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.85 y[1] (analytic) = -2.229724410217487582807432708537 y[1] (numeric) = -2.2297244102174875828074327085369 absolute error = 1e-31 relative error = 4.4848591844696173984739167657125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.722 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.86 y[1] (analytic) = -2.220619671819408461617705871402 y[1] (numeric) = -2.2206196718194084616177058714024 absolute error = 4e-31 relative error = 1.8012990025989913674717026828372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.34 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.87 y[1] (analytic) = -2.211510910895074441543251931852 y[1] (numeric) = -2.2115109108950744415432519318524 absolute error = 4e-31 relative error = 1.8087181846102954929581673693078e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.88 y[1] (analytic) = -2.202398129061906701404306964037 y[1] (numeric) = -2.2023981290619067014043069640377 absolute error = 7e-31 relative error = 3.1783535899486039807427318593624e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.89 y[1] (analytic) = -2.193281327936026242119565503583 y[1] (numeric) = -2.1932813279360262421195655035835 absolute error = 5e-31 relative error = 2.2796893113138472366754250345070e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.9 y[1] (analytic) = -2.184160509132255453815109683955 y[1] (numeric) = -2.1841605091322554538151096839555 absolute error = 5e-31 relative error = 2.2892090480962173730366532874814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=44014516, alloc=4455632, time=1.74 x[1] = 22.91 y[1] (analytic) = -2.175035674264119680415893971324 y[1] (numeric) = -2.175035674264119680415893971324 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.92 y[1] (analytic) = -2.165906824943848781724838578631 y[1] (numeric) = -2.165906824943848781724838578631 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.93 y[1] (analytic) = -2.156773962782378692994572473238 y[1] (numeric) = -2.1567739627823786929945724732381 absolute error = 1e-31 relative error = 4.6365544895114319627055701055590e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.94 y[1] (analytic) = -2.147637089389352981996854760366 y[1] (numeric) = -2.1476370893893529819968547603659 absolute error = 1e-31 relative error = 4.6562801738739498129841360106750e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.95 y[1] (analytic) = -2.138496206373124403594691126421 y[1] (numeric) = -2.1384962063731244035946911264209 absolute error = 1e-31 relative error = 4.6761831843321034810601671414206e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 15.16 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.96 y[1] (analytic) = -2.129351315340756451822149962132 y[1] (numeric) = -2.1293513153407564518221499621323 absolute error = 3e-31 relative error = 1.4088797740357443680708870481154e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.97 y[1] (analytic) = -2.120202417898024909476870755084 y[1] (numeric) = -2.1202024178980249094768707550842 absolute error = 2e-31 relative error = 9.4330615941038594315804590898511e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 22.98 y[1] (analytic) = -2.111049515649419395230245344614 y[1] (numeric) = -2.1110495156494193952302453446142 absolute error = 2e-31 relative error = 9.4739606303585097183272002293257e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 22.99 y[1] (analytic) = -2.101892610198144908260240669053 y[1] (numeric) = -2.1018926101981449082602406690535 absolute error = 5e-31 relative error = 2.3788084965618920029791925849483e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23 y[1] (analytic) = -2.0927317031461233704118197058 y[1] (numeric) = -2.0927317031461233704118197057999 absolute error = 1e-31 relative error = 4.7784434024516508912043950401864e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.01 y[1] (analytic) = -2.083566796093995165889905408628 y[1] (numeric) = -2.0835667960939951658899054086278 absolute error = 2e-31 relative error = 9.5989243241413929288723804443160e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.02 y[1] (analytic) = -2.074397890641120678489820583855 y[1] (numeric) = -2.0743978906411206784898205838557 absolute error = 7e-31 relative error = 3.3744731575274382291722836194588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.03 y[1] (analytic) = -2.06522498838558182637012481739 y[1] (numeric) = -2.0652249883855818263701248173899 absolute error = 1e-31 relative error = 4.8420874511193833556082876952477e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.04 y[1] (analytic) = -2.056048090924183594372757768151 y[1] (numeric) = -2.0560480909241835943727577681509 absolute error = 1e-31 relative error = 4.8636994650767379407047434802968e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.05 y[1] (analytic) = -2.046867199852455563895386379848 y[1] (numeric) = -2.0468671998524555638953863798482 absolute error = 2e-31 relative error = 9.7710296014522393307722934893950e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.06 y[1] (analytic) = -2.037682316764653440320841832406 y[1] (numeric) = -2.0376823167646534403208418324064 absolute error = 4e-31 relative error = 1.9630145322903092733540740782904e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.07 y[1] (analytic) = -2.028493443253760578008520356445 y[1] (numeric) = -2.028493443253760578008520356445 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.08 y[1] (analytic) = -2.01930058091148950285261036898 y[1] (numeric) = -2.0193005809114895028526103689799 absolute error = 1e-31 relative error = 4.9522097376340637748056662173571e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.09 y[1] (analytic) = -2.010103731328283432411996755837 y[1] (numeric) = -2.0101037313282834324119967558375 absolute error = 5e-31 relative error = 2.4874338185004924445687617018932e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.1 y[1] (analytic) = -2.000902896093317793616681526048 y[1] (numeric) = -2.0009028960933177936166815260481 absolute error = 1e-31 relative error = 4.9977437783335696554184075717010e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.11 y[1] (analytic) = -1.991698076794501738055548495616 y[1] (numeric) = -1.9916980767945017380555484956163 absolute error = 3e-31 relative error = 1.5062523958592606751805103092172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.12 y[1] (analytic) = -1.982489275018479654850288122441 y[1] (numeric) = -1.982489275018479654850288122441 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.13 y[1] (analytic) = -1.973276492350632681120287110681 y[1] (numeric) = -1.9732764923506326811202871106817 absolute error = 7e-31 relative error = 3.5473994785501989398002899428188e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.14 y[1] (analytic) = -1.964059730375080210043275931431 y[1] (numeric) = -1.9640597303750802100432759314309 absolute error = 1e-31 relative error = 5.0914948488304279028552892665071e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.15 y[1] (analytic) = -1.954838990674681396516515967061 y[1] (numeric) = -1.9548389906746813965165159670613 absolute error = 3e-31 relative error = 1.5346532447486112427419940057932e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.16 y[1] (analytic) = -1.945614274831036660423296578961 y[1] (numeric) = -1.9456142748310366604232965789615 absolute error = 5e-31 relative error = 2.5698824606096272206186391171717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.17 y[1] (analytic) = -1.936385584424489187509501022458 y[1] (numeric) = -1.936385584424489187509501022458 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.18 y[1] (analytic) = -1.927152921034126427874988788444 y[1] (numeric) = -1.927152921034126427874988788444 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.19 y[1] (analytic) = -1.917916286237781592084530638493 y[1] (numeric) = -1.9179162862377815920845306384936 absolute error = 6e-31 relative error = 3.1283951458432556537307975333895e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=48016264, alloc=4455632, time=1.90 TOP MAIN SOLVE Loop x[1] = 23.2 y[1] (analytic) = -1.908675681612035144903021318936 y[1] (numeric) = -1.9086756816120351449030213189366 absolute error = 6e-31 relative error = 3.1435408633343626240714829093538e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.21 y[1] (analytic) = -1.8994311087322162966596836894 y[1] (numeric) = -1.8994311087322162966596836893998 absolute error = 2e-31 relative error = 1.0529468485618880145067780839197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 72.72 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.22 y[1] (analytic) = -1.890182569172404492245966782593 y[1] (numeric) = -1.8901825691724044922459667825927 absolute error = 3e-31 relative error = 1.5871482728324580734736724315676e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.23 y[1] (analytic) = -1.880930064505430897751829124522 y[1] (numeric) = -1.8809300645054308977518291245223 absolute error = 3e-31 relative error = 1.5949556321163996999013738953788e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.24 y[1] (analytic) = -1.871673596302879884745087487772 y[1] (numeric) = -1.8716735963028798847450874877719 absolute error = 1e-31 relative error = 5.3428119196386685264566613269414e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.25 y[1] (analytic) = -1.862413166135090512198500124865 y[1] (numeric) = -1.8624131661350905121985001248653 absolute error = 3e-31 relative error = 1.6108133547109999322545096070672e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.26 y[1] (analytic) = -1.853148775571158006069242433974 y[1] (numeric) = -1.8531487755711580060692424339741 absolute error = 1e-31 relative error = 5.3962208171429222015762390554393e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.27 y[1] (analytic) = -1.8438804261789352365354219452 y[1] (numeric) = -1.8438804261789352365354219452006 absolute error = 6e-31 relative error = 3.2540071009017498348953148271127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.04 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.28 y[1] (analytic) = -1.834608119525034192894268482299 y[1] (numeric) = -1.8346081195250341928942684822988 absolute error = 2e-31 relative error = 1.0901510675303151289097700870638e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.29 y[1] (analytic) = -1.825331857174827456126624351871 y[1] (numeric) = -1.8253318571748274561266243518712 absolute error = 2e-31 relative error = 1.0956911709717906380015585355658e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.65 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.3 y[1] (analytic) = -1.816051640692449669132348439713 y[1] (numeric) = -1.8160516406924496691323484397133 absolute error = 3e-31 relative error = 1.6519354035858351893335896202193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.31 y[1] (analytic) = -1.806767471640799004641237151967 y[1] (numeric) = -1.8067674716407990046412371519673 absolute error = 3e-31 relative error = 1.6604239599662362856272468187440e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.32 y[1] (analytic) = -1.797479351581538630804054227001 y[1] (numeric) = -1.7974793515815386308040542270017 absolute error = 7e-31 relative error = 3.8943423710770013010523126693900e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.33 y[1] (analytic) = -1.788187282075098174468250562351 y[1] (numeric) = -1.7881872820750981744682505623513 absolute error = 3e-31 relative error = 1.6776766226178816701221438196325e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.95 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.34 y[1] (analytic) = -1.778891264680675182142944349545 y[1] (numeric) = -1.7788912646806751821429443495447 absolute error = 3e-31 relative error = 1.6864437189411480602087602339140e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.43 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.35 y[1] (analytic) = -1.769591300956236578657720988114 y[1] (numeric) = -1.7695913009562365786577209881145 absolute error = 5e-31 relative error = 2.8255111772408368299030814089644e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 20 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.36 y[1] (analytic) = -1.760287392458520123519801458436 y[1] (numeric) = -1.7602873924585201235198014584357 absolute error = 3e-31 relative error = 1.7042671627671120705369922892066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.37 y[1] (analytic) = -1.750979540743035864974117071174 y[1] (numeric) = -1.7509795407430358649741170711742 absolute error = 2e-31 relative error = 1.1422178006439134111811016270218e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.38 y[1] (analytic) = -1.74166774736406759177081777896 y[1] (numeric) = -1.7416677473640675917708177789602 absolute error = 2e-31 relative error = 1.1483246463206924227683648107361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.59 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.39 y[1] (analytic) = -1.732352013874674282644730533332 y[1] (numeric) = -1.7323520138746742826447305333319 absolute error = 1e-31 relative error = 5.7724988454473794716517457197470e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.4 y[1] (analytic) = -1.723032341826691553511273496934 y[1] (numeric) = -1.7230323418266915535112734969343 absolute error = 3e-31 relative error = 1.7411164765598753872424509582051e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.41 y[1] (analytic) = -1.713708732770733102383321277309 y[1] (numeric) = -1.7137087327707331023833212773087 absolute error = 3e-31 relative error = 1.7505892002718481536427983498064e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 0.113 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.42 y[1] (analytic) = -1.704381188256192152013505734285 y[1] (numeric) = -1.7043811882561921520135057342852 absolute error = 2e-31 relative error = 1.1734464178440417267384175646815e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.76 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.43 y[1] (analytic) = -1.695049709831242890266426327889 y[1] (numeric) = -1.6950497098312428902664263278894 absolute error = 4e-31 relative error = 2.3598127988814175765096133991277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.44 y[1] (analytic) = -1.685714299042841908225233417718 y[1] (numeric) = -1.6857142990428419082252334177184 absolute error = 4e-31 relative error = 2.3728813371703749399847605155098e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.45 y[1] (analytic) = -1.676374957436729636037037397824 y[1] (numeric) = -1.6763749574367296360370373978239 absolute error = 1e-31 relative error = 5.9652525562005263374150590807279e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.46 y[1] (analytic) = -1.667031686557431776501586053181 y[1] (numeric) = -1.6670316865574317765015860531815 absolute error = 5e-31 relative error = 2.9993431080637964807911931523422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.47 y[1] (analytic) = -1.657684487948260736407642054727 y[1] (numeric) = -1.6576844879482607364076420547267 absolute error = 3e-31 relative error = 1.8097533166357501101781204013089e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.04 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop bytes used=52017584, alloc=4455632, time=2.06 x[1] = 23.48 y[1] (analytic) = -1.648333363151317055621482069615 y[1] (numeric) = -1.6483333631513170556214820696155 absolute error = 5e-31 relative error = 3.0333669825385921279704393298381e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.49 y[1] (analytic) = -1.638978313707490833931928551723 y[1] (numeric) = -1.6389783137074908339319285517232 absolute error = 2e-31 relative error = 1.2202723997463097989627685826814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.5 y[1] (analytic) = -1.629619341156463155656314894346 y[1] (numeric) = -1.6296193411564631556563148943458 absolute error = 2e-31 relative error = 1.2272804755622839799850793461060e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.04 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.51 y[1] (analytic) = -1.620256447036707512011774272521 y[1] (numeric) = -1.6202564470367075120117742725211 absolute error = 1e-31 relative error = 6.1718624963900213280735948489177e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.52 y[1] (analytic) = -1.610889632885491221256232176251 y[1] (numeric) = -1.6108896328854912212562321762509 absolute error = 1e-31 relative error = 6.2077499264102855287417175746835e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.53 y[1] (analytic) = -1.601518900238876846603472338096 y[1] (numeric) = -1.6015189002388768466034723380963 absolute error = 3e-31 relative error = 1.8732217269196952348700426899093e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.54 y[1] (analytic) = -1.592144250631723611916635489042 y[1] (numeric) = -1.5921442506317236119166354890422 absolute error = 2e-31 relative error = 1.2561675860754760602576048967228e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.86 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.55 y[1] (analytic) = -1.582765685597688815184500135099 y[1] (numeric) = -1.5827656855976888151845001350995 absolute error = 5e-31 relative error = 3.1590272934884134285609129813952e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.56 y[1] (analytic) = -1.573383206669229239784884333742 y[1] (numeric) = -1.5733832066692292397848843337425 absolute error = 5e-31 relative error = 3.1778653660507417268944390513409e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 27.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.57 y[1] (analytic) = -1.563996815377602563539497263882 y[1] (numeric) = -1.5639968153776025635394972638817 absolute error = 3e-31 relative error = 1.9181624735442296490254910042826e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.58 y[1] (analytic) = -1.554606513252868765564559225556 y[1] (numeric) = -1.554606513252868765564559225556 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.58 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.59 y[1] (analytic) = -1.545212301823891530921498575809 y[1] (numeric) = -1.545212301823891530921498575809 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.6 y[1] (analytic) = -1.535814182618339653072024005205 y[1] (numeric) = -1.535814182618339653072024005205 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.61 y[1] (analytic) = -1.526412157162688434141860485052 y[1] (numeric) = -1.5264121571626884341418604850519 absolute error = 1e-31 relative error = 6.5513105048823176742974370174183e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.62 y[1] (analytic) = -1.517006226982221082997427168548 y[1] (numeric) = -1.5170062269822210829974271685482 absolute error = 2e-31 relative error = 1.3183861505819906419860323346403e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.63 y[1] (analytic) = -1.507596393601030111139725509671 y[1] (numeric) = -1.507596393601030111139725509671 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.76 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.64 y[1] (analytic) = -1.498182658542018726419695871585 y[1] (numeric) = -1.4981826585420187264196958715851 absolute error = 1e-31 relative error = 6.6747535375503983362832207001945e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 94.36 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.65 y[1] (analytic) = -1.488765023326902224579290931598 y[1] (numeric) = -1.4887650233269022245792909315984 absolute error = 4e-31 relative error = 2.6867906871302699508666473387351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.66 y[1] (analytic) = -1.479343489476209378622504252126 y[1] (numeric) = -1.4793434894762093786225042521262 absolute error = 2e-31 relative error = 1.3519510608777811880925217647919e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.67 y[1] (analytic) = -1.469918058509283826020582476673 y[1] (numeric) = -1.4699180585092838260205824766733 absolute error = 3e-31 relative error = 2.0409300930981469128576636281295e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.68 y[1] (analytic) = -1.460488731944285453755639726417 y[1] (numeric) = -1.4604887319442854537556397264174 absolute error = 4e-31 relative error = 2.7388092167441600725480795055450e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.69 y[1] (analytic) = -1.451055511298191781206882916489 y[1] (numeric) = -1.4510555112981917812068829164887 absolute error = 3e-31 relative error = 2.0674605324478866620385511370570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.7 y[1] (analytic) = -1.441618398086799340883646881412 y[1] (numeric) = -1.4416183980867993408836468814121 absolute error = 1e-31 relative error = 6.9366484315621945109213420245897e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.71 y[1] (analytic) = -1.43217739382472505700942839632 y[1] (numeric) = -1.4321773938247250570094283963204 absolute error = 4e-31 relative error = 2.7929501032813636004983277075548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.72 y[1] (analytic) = -1.422732500025407621961098404382 y[1] (numeric) = -1.4227325000254076219610984043816 absolute error = 4e-31 relative error = 2.8114912676336322483144479610361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.73 y[1] (analytic) = -1.413283718201108870567462011324 y[1] (numeric) = -1.4132837182011088705674620113243 absolute error = 3e-31 relative error = 2.1227160274785695770524225460014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.014 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.74 y[1] (analytic) = -1.403831049862915152271326084908 y[1] (numeric) = -1.4038310498629151522713260849078 absolute error = 2e-31 relative error = 1.4246728623044069743237077209552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.75 y[1] (analytic) = -1.394374496520738701159224600592 y[1] (numeric) = -1.3943744965207387011592246005924 absolute error = 4e-31 relative error = 2.8686697942201695413848768521971e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.76 y[1] (analytic) = -1.38491405968331900386294220443 y[1] (numeric) = -1.3849140596833190038629422044302 absolute error = 2e-31 relative error = 1.4441329308602220812886714006625e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 97.95 Order of pole (six term test) = -0.5 bytes used=56021592, alloc=4455632, time=2.22 TOP MAIN SOLVE Loop x[1] = 23.77 y[1] (analytic) = -1.375449740858224165336966820242 y[1] (numeric) = -1.3754497408582241653369668202418 absolute error = 2e-31 relative error = 1.4540698511834260956903133247340e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.78 y[1] (analytic) = -1.365981541551852272515992510383 y[1] (numeric) = -1.3659815415518522725159925103833 absolute error = 3e-31 relative error = 2.1962229420697635755731211590932e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.62 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.79 y[1] (analytic) = -1.356509463269432755856584207765 y[1] (numeric) = -1.3565094632694327558565842077646 absolute error = 4e-31 relative error = 2.9487446334206012148550520323244e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.8 y[1] (analytic) = -1.347033507515027748767106371168 y[1] (numeric) = -1.3470335075150277487671063711682 absolute error = 2e-31 relative error = 1.4847440608137118959311695029081e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.81 y[1] (analytic) = -1.337553675791533444930008076261 y[1] (numeric) = -1.3375536757915334449300080762606 absolute error = 4e-31 relative error = 2.9905341911851815363373868840372e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.82 y[1] (analytic) = -1.328069969600681453520547540903 y[1] (numeric) = -1.3280699696006814535205475409036 absolute error = 6e-31 relative error = 4.5178342537208751188244258584024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.83 y[1] (analytic) = -1.31858239044304015232602959538 y[1] (numeric) = -1.3185823904430401523260295953802 absolute error = 2e-31 relative error = 1.5167804564172932383419269764178e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.84 y[1] (analytic) = -1.30909093981801603876962014587 y[1] (numeric) = -1.3090909398180160387696201458704 absolute error = 4e-31 relative error = 3.0555554838352651731800629942124e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.85 y[1] (analytic) = -1.299595619223855078842792242866 y[1] (numeric) = -1.2995956192238550788427922428663 absolute error = 3e-31 relative error = 2.3084103667505904506665835549197e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.86 y[1] (analytic) = -1.290096430157644053950448955122 y[1] (numeric) = -1.2900964301576440539504489551223 absolute error = 3e-31 relative error = 2.3254075663424735809514060022555e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.87 y[1] (analytic) = -1.28059337411531190567275886412 y[1] (numeric) = -1.2805933741153119056727588641197 absolute error = 3e-31 relative error = 2.3426640029841845405838559508986e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 4.408 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.88 y[1] (analytic) = -1.271086452591631078447730633802 y[1] (numeric) = -1.2710864525916310784477306338017 absolute error = 3e-31 relative error = 2.3601856458176149461689572495867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.89 y[1] (analytic) = -1.261575667080218860178543775431 y[1] (numeric) = -1.261575667080218860178543775431 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.9 y[1] (analytic) = -1.252061019073538720769643417757 y[1] (numeric) = -1.2520610190735387207696434177573 absolute error = 3e-31 relative error = 2.3960493572588394714381397254807e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.91 y[1] (analytic) = -1.242542510062901648595597608177 y[1] (numeric) = -1.2425425100629016485955976081771 absolute error = 1e-31 relative error = 8.0480143890560063228800807123264e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.92 y[1] (analytic) = -1.233020141538467484906706411149 y[1] (numeric) = -1.2330201415384674849067064111491 absolute error = 1e-31 relative error = 8.1101675983352314527622662525267e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.93 y[1] (analytic) = -1.223493914989246256175342835712 y[1] (numeric) = -1.2234939149892462561753428357122 absolute error = 2e-31 relative error = 1.6346628091056576649086290707858e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.94 y[1] (analytic) = -1.213963831903099504386996414471 y[1] (numeric) = -1.2139638319030995043869964144707 absolute error = 3e-31 relative error = 2.4712433115053996943668363228670e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.95 y[1] (analytic) = -1.204429893766741615279981071775 y[1] (numeric) = -1.204429893766741615279981071775 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.96 y[1] (analytic) = -1.194892102065741144537759758972 y[1] (numeric) = -1.1948921020657411445377597589717 absolute error = 3e-31 relative error = 2.5106869438785064182585222119562e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.26 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.97 y[1] (analytic) = -1.185350458284522141937829199436 y[1] (numeric) = -1.1853504582845221419378291994355 absolute error = 5e-31 relative error = 4.2181617808088277425577915734013e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.46 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 23.98 y[1] (analytic) = -1.175804963906365473461098975562 y[1] (numeric) = -1.1758049639063654734610989755621 absolute error = 1e-31 relative error = 8.5048118582329305692981165833055e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 23.99 y[1] (analytic) = -1.166255620413410141365690103912 y[1] (numeric) = -1.1662556204134101413656901039126 absolute error = 6e-31 relative error = 5.1446697404751981862349868880703e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24 y[1] (analytic) = -1.156702429286654602229069183183 y[1] (numeric) = -1.1567024292866546022290691831827 absolute error = 3e-31 relative error = 2.5935797522705283674678994722861e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 20.96 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.01 y[1] (analytic) = -1.147145392005958082962425162551 y[1] (numeric) = -1.1471453920059580829624251625512 absolute error = 2e-31 relative error = 1.7434581648823921106001471692361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.02 y[1] (analytic) = -1.137584510050041894801186765162 y[1] (numeric) = -1.1375845100500418948011867651623 absolute error = 3e-31 relative error = 2.6371667102499762245465867942335e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.03 y[1] (analytic) = -1.128019784896490745275569612945 y[1] (numeric) = -1.1280197848964907452755696129454 absolute error = 4e-31 relative error = 3.5460370939921480693038661135038e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.04 y[1] (analytic) = -1.118451218021754048165033134595 y[1] (numeric) = -1.1184512180217540481650331345949 absolute error = 1e-31 relative error = 8.9409353209765993230712625226156e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=60022764, alloc=4455632, time=2.38 x[1] = 24.05 y[1] (analytic) = -1.108878810901147231440518398251 y[1] (numeric) = -1.1088788109011472314405183982514 absolute error = 4e-31 relative error = 3.6072472128395520165347115693588e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.91 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.06 y[1] (analytic) = -1.099302565008853043198329094166 y[1] (numeric) = -1.0993025650088530431983290941661 absolute error = 1e-31 relative error = 9.0966766732864547882230788935787e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.07 y[1] (analytic) = -1.089722481817922855589509000323 y[1] (numeric) = -1.0897224818179228555895090003227 absolute error = 3e-31 relative error = 2.7529945009441930347452475849250e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.08 y[1] (analytic) = -1.080138562800277966748560395559 y[1] (numeric) = -1.0801385628002779667485603955586 absolute error = 4e-31 relative error = 3.7032285835901743860889062595451e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.37 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.09 y[1] (analytic) = -1.0705508094267109007253390401 y[1] (numeric) = -1.0705508094267109007253390400995 absolute error = 5e-31 relative error = 4.6704929424858804153035868314373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.1 y[1] (analytic) = -1.060959223166886705423952522522 y[1] (numeric) = -1.0609592231668867054239525225221 absolute error = 1e-31 relative error = 9.4254329305425346691456458171085e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.11 y[1] (analytic) = -1.05136380548934424855247997492 y[1] (numeric) = -1.0513638054893442485524799749204 absolute error = 4e-31 relative error = 3.8045821808924167706487145794255e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.12 y[1] (analytic) = -1.041764557861497511587322384394 y[1] (numeric) = -1.041764557861497511587322384394 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.13 y[1] (analytic) = -1.032161481749636881755983978836 y[1] (numeric) = -1.0321614817496368817559839788359 absolute error = 1e-31 relative error = 9.6884064914424113919929137958273e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.14 y[1] (analytic) = -1.022554578618930442042076438293 y[1] (numeric) = -1.0225545786189304420420764382935 absolute error = 5e-31 relative error = 4.8897145487852940920095764238515e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.736 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.15 y[1] (analytic) = -1.012943849933425259216328979846 y[1] (numeric) = -1.0129438499334252592163289798462 absolute error = 2e-31 relative error = 1.9744431047500293702270267127351e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.16 y[1] (analytic) = -1.003329297156048669897378683905 y[1] (numeric) = -1.0033292971560486698973786839053 absolute error = 3e-31 relative error = 2.9900452508498886339924158397651e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.182 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.17 y[1] (analytic) = -0.993710921748609564646106773036 y[1] (numeric) = -0.9937109217486095646461067730362 absolute error = 2.0e-31 relative error = 2.0126577621594893882505464973796e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 15.06 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.18 y[1] (analytic) = -0.984088725171799670097277920747 y[1] (numeric) = -0.984088725171799670097277920747 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 53.18 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.19 y[1] (analytic) = -0.974462708885194829132231057121 y[1] (numeric) = -0.97446270888519482913223105712097 absolute error = 3e-32 relative error = 3.0786196050868494032836910650227e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.2 y[1] (analytic) = -0.964832874347256279096361550615 y[1] (numeric) = -0.96483287434725627909636155061496 absolute error = 4e-32 relative error = 4.1457957189799758053573417340956e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.21 y[1] (analytic) = -0.955199223015331928065126080735 y[1] (numeric) = -0.95519922301533192806512608073545 absolute error = 4.5e-31 relative error = 4.7110591084806298891202280399040e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.2 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.22 y[1] (analytic) = -0.945561756345657629162292974567 y[1] (numeric) = -0.94556175634565762916229297456729 absolute error = 2.9e-31 relative error = 3.0669599109081161997204371606682e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.23 y[1] (analytic) = -0.935920475793358452934152261197 y[1] (numeric) = -0.93592047579335845293415226119725 absolute error = 2.5e-31 relative error = 2.6711671179977198252199267855756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.24 y[1] (analytic) = -0.926275382812449957783391201876 y[1] (numeric) = -0.92627538281244995778339120187633 absolute error = 3.3e-31 relative error = 3.5626554059767948856243947459444e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.25 y[1] (analytic) = -0.916626478855839458466332580232 y[1] (numeric) = -0.91662647885583945846633258023171 absolute error = 2.9e-31 relative error = 3.1637750674842675224738376688540e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.26 y[1] (analytic) = -0.906973765375327292657224585902 y[1] (numeric) = -0.90697376537532729265722458590221 absolute error = 2.1e-31 relative error = 2.3153922198962062664147244524004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.27 y[1] (analytic) = -0.897317243821608085583262696561 y[1] (numeric) = -0.8973172438216080855832626965613 absolute error = 3.0e-31 relative error = 3.3432991739055641508444140926842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.28 y[1] (analytic) = -0.887656915644272012734015557341 y[1] (numeric) = -0.88765691564427201273401555734074 absolute error = 2.6e-31 relative error = 2.9290595884254322330686508051910e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.29 y[1] (analytic) = -0.877992782291806060648918473107 y[1] (numeric) = -0.87799278229180606064891847310704 absolute error = 4e-32 relative error = 4.5558461079359721824233590625409e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.44 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.3 y[1] (analytic) = -0.868324845211595285786489767804 y[1] (numeric) = -0.86832484521159528578648976780424 absolute error = 2.4e-31 relative error = 2.7639425650836499824483099834456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.31 y[1] (analytic) = -0.858653105849924071478916926092 y[1] (numeric) = -0.8586531058499240714789169260922 absolute error = 2.0e-31 relative error = 2.3292293318153574054744427458430e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.32 y[1] (analytic) = -0.848977565651977382975651115712 y[1] (numeric) = -0.84897756565197738297565111571175 absolute error = 2.5e-31 relative error = 2.9447185663617743485408111351387e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.85 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.33 y[1] (analytic) = -0.839298226061842020579640394329 y[1] (numeric) = -0.83929822606184202057964039432928 absolute error = 2.8e-31 relative error = 3.3361204790556623536555407393451e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=64027508, alloc=4455632, time=2.54 TOP MAIN SOLVE Loop x[1] = 24.34 y[1] (analytic) = -0.829615088522507870879823631987 y[1] (numeric) = -0.82961508852250787087982363198671 absolute error = 2.9e-31 relative error = 3.4955969824086939258603467374392e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.35 y[1] (analytic) = -0.819928154475869156083498929641 y[1] (numeric) = -0.81992815447586915608349892964103 absolute error = 3e-32 relative error = 3.6588571615981645268400128369793e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.36 y[1] (analytic) = -0.810237425362725681452172085554 y[1] (numeric) = -0.81023742536272568145217208555397 absolute error = 3e-32 relative error = 3.7026184005965476323020573501847e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.37 y[1] (analytic) = -0.80054290262278408084448245442 y[1] (numeric) = -0.80054290262278408084448245442055 absolute error = 5.5e-31 relative error = 6.8703375946255821228177154440289e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.38 y[1] (analytic) = -0.790844587694659060369795359039 y[1] (numeric) = -0.79084458769465906036979535903883 absolute error = 1.7e-31 relative error = 2.1496005997278963069170896027043e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.39 y[1] (analytic) = -0.781142482015874640156042050956 y[1] (numeric) = -0.78114248201587464015604205095607 absolute error = 7e-32 relative error = 8.9612332719829513080469221529189e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.4 y[1] (analytic) = -0.771436587022865394235380074813 y[1] (numeric) = -0.77143658702286539423538007481283 absolute error = 1.7e-31 relative error = 2.2036808061705426600384593346543e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.41 y[1] (analytic) = -0.761726904150977688551238770981 y[1] (numeric) = -0.76172690415097768855123877098093 absolute error = 7e-32 relative error = 9.1896452151735585891911005303125e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 58.62 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.42 y[1] (analytic) = -0.752013434834470917090306552488 y[1] (numeric) = -0.75201343483447091709030655248788 absolute error = 1.2e-31 relative error = 1.5957161726294656353307325142360e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.43 y[1] (analytic) = -0.742296180506518736143008515074 y[1] (numeric) = -0.74229618050651873614300851507443 absolute error = 4.3e-31 relative error = 5.7928359500190611999546610597037e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.44 y[1] (analytic) = -0.732575142599210296696014883478 y[1] (numeric) = -0.73257514259921029669601488347845 absolute error = 4.5e-31 relative error = 6.1427145671825460079283088161890e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.45 y[1] (analytic) = -0.722850322543551474960312762612 y[1] (numeric) = -0.72285032254355147496031276261234 absolute error = 3.4e-31 relative error = 4.7036016917529302322450544521032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.46 y[1] (analytic) = -0.713121721769466101038365649138 y[1] (numeric) = -0.71312172176946610103836564913839 absolute error = 3.9e-31 relative error = 5.4689120818293761430289382951821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 19.06 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.47 y[1] (analytic) = -0.703389341705797185733877166983 y[1] (numeric) = -0.70338934170579718573387716698272 absolute error = 2.8e-31 relative error = 3.9807256578692099252287004278985e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 28.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.39 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.48 y[1] (analytic) = -0.693653183780308145507667519499 y[1] (numeric) = -0.69365318378030814550766751949907 absolute error = 7e-32 relative error = 1.0091498408255010619133789820556e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.49 y[1] (analytic) = -0.683913249419684025583163201236 y[1] (numeric) = -0.68391324941968402558316320123567 absolute error = 3.3e-31 relative error = 4.8251733722078424233233797243756e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.5 y[1] (analytic) = -0.674169540049532721204992583507 y[1] (numeric) = -0.67416954004953272120499258350737 absolute error = 3.7e-31 relative error = 5.4882337159999142788882686715079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.51 y[1] (analytic) = -0.664422057094386197054172080168 y[1] (numeric) = -0.66442205709438619705417208016825 absolute error = 2.5e-31 relative error = 3.7626685828776693090533053955757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.52 y[1] (analytic) = -0.654670801977701704823359713053 y[1] (numeric) = -0.65467080197770170482335971305345 absolute error = 4.5e-31 relative error = 6.8736836688086654999438135588569e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.53 y[1] (analytic) = -0.64491577612186299895564503045 y[1] (numeric) = -0.64491577612186299895564503045031 absolute error = 3.1e-31 relative error = 4.8068292244943088122494402022376e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.54 y[1] (analytic) = -0.635156980948181550550336486605 y[1] (numeric) = -0.63515698094818155055033648660511 absolute error = 1.1e-31 relative error = 1.7318553255258042383696786219810e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 52.92 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.55 y[1] (analytic) = -0.62539441787689775943919956561 y[1] (numeric) = -0.62539441787689775943919956561031 absolute error = 3.1e-31 relative error = 4.9568718737911761051831245651127e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.56 y[1] (analytic) = -0.615628088327182164436591128986 y[1] (numeric) = -0.61562808832718216443659112898556 absolute error = 4.4e-31 relative error = 7.1471722675226161999138211891261e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.57 y[1] (analytic) = -0.605857993717136651766927682802 y[1] (numeric) = -0.60585799371713665176692768280242 absolute error = 4.2e-31 relative error = 6.9323175456209273884223265260147e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.58 y[1] (analytic) = -0.596084135463795661672917497245 y[1] (numeric) = -0.59608413546379566167291749724478 absolute error = 2.2e-31 relative error = 3.6907541555157213408649370873552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 86.35 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.59 y[1] (analytic) = -0.586306514983127393207978768984 y[1] (numeric) = -0.58630651498312739320797876898381 absolute error = 1.9e-31 relative error = 3.2406257673167384202306321192115e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.9 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.6 y[1] (analytic) = -0.576525133690035007216258294615 y[1] (numeric) = -0.57652513369003500721625829461526 absolute error = 2.6e-31 relative error = 4.5097773680026118502740094648750e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 137.1 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.61 y[1] (analytic) = -0.566739992998357827503657421598 y[1] (numeric) = -0.56673999299835782750365742159774 absolute error = 2.6e-31 relative error = 4.5876416559992682551883320481889e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=68029084, alloc=4455632, time=2.70 x[1] = 24.62 y[1] (analytic) = -0.556951094320872540203264361581 y[1] (numeric) = -0.55695109432087254020326436158151 absolute error = 5.1e-31 relative error = 9.1569978980268792215069478688929e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.63 y[1] (analytic) = -0.547158439069294391338584289668 y[1] (numeric) = -0.54715843906929439133858428966771 absolute error = 2.9e-31 relative error = 5.3001101562699868962339487813779e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.64 y[1] (analytic) = -0.537362028654278382587951011927 y[1] (numeric) = -0.53736202865427838258795101192707 absolute error = 7e-32 relative error = 1.3026599623218962296866062308087e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.65 y[1] (analytic) = -0.527561864485420465253496362374 y[1] (numeric) = -0.52756186448542046525349636237444 absolute error = 4.4e-31 relative error = 8.3402540937861838653711575775431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.66 y[1] (analytic) = -0.517757947971258732438045889481 y[1] (numeric) = -0.51775794797125873243804588948101 absolute error = 1e-32 relative error = 1.9314044408556544491809109564787e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.67 y[1] (analytic) = -0.507950280519274609433301811149 y[1] (numeric) = -0.50795028051927460943330181114917 absolute error = 1.7e-31 relative error = 3.3467842527069773725059457691356e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 115.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.68 y[1] (analytic) = -0.498138863535894042322666655816 y[1] (numeric) = -0.49813886353589404232266665581645 absolute error = 4.5e-31 relative error = 9.0336256200892598287814383613714e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.69 y[1] (analytic) = -0.488323698426488684802053465935 y[1] (numeric) = -0.48832369842648868480205346593462 absolute error = 3.8e-31 relative error = 7.7817235007119867008545496070378e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.7 y[1] (analytic) = -0.478504786595377083222020918429 y[1] (numeric) = -0.47850478659537708322202091842872 absolute error = 2.8e-31 relative error = 5.8515611096021819398680803464498e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.634 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.71 y[1] (analytic) = -0.468682129445825859854564214819 y[1] (numeric) = -0.46868212944582585985456421481908 absolute error = 8e-32 relative error = 1.7069138115974839788417025000811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.72 y[1] (analytic) = -0.458855728380050894387885111428 y[1] (numeric) = -0.4588557283800508943878851114283 absolute error = 3.0e-31 relative error = 6.5380027194849057631232979440005e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.73 y[1] (analytic) = -0.449025584799218503652456997436 y[1] (numeric) = -0.44902558479921850365245699743578 absolute error = 2.2e-31 relative error = 4.8994981009461377575175606874069e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.74 y[1] (analytic) = -0.439191700103446619581693485426 y[1] (numeric) = -0.43919170010344661958169348542621 absolute error = 2.1e-31 relative error = 4.7815111248809320340953777853016e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.87 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.75 y[1] (analytic) = -0.429354075691805965410521555447 y[1] (numeric) = -0.42935407569180596541052155544661 absolute error = 3.9e-31 relative error = 9.0834120852726070740714067219323e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.76 y[1] (analytic) = -0.419512712962321230115152889381 y[1] (numeric) = -0.41951271296232123011515288938121 absolute error = 2.1e-31 relative error = 5.0058077743846887405741607398473e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.77 y[1] (analytic) = -0.409667613311972241097339647616 y[1] (numeric) = -0.40966761331197224109733964761647 absolute error = 4.7e-31 relative error = 1.1472715555917844099987467827550e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.78 y[1] (analytic) = -0.399818778136695135116393574442 y[1] (numeric) = -0.39981877813669513511639357444155 absolute error = 4.5e-31 relative error = 1.1255099175110486425202025389866e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.79 y[1] (analytic) = -0.389966208831383527472239972356 y[1] (numeric) = -0.38996620883138352747223997235583 absolute error = 1.7e-31 relative error = 4.3593520707714923286598791538217e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.8 y[1] (analytic) = -0.380109906789889679442770758376 y[1] (numeric) = -0.38010990678988967944277075837596 absolute error = 4e-32 relative error = 1.0523272160362418775169451424339e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.81 y[1] (analytic) = -0.370249873405025663978753507494 y[1] (numeric) = -0.37024987340502566397875350749411 absolute error = 1.1e-31 relative error = 2.9709665796338633407852870288032e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.82 y[1] (analytic) = -0.360386110068564529659546099579 y[1] (numeric) = -0.36038611006856452965954609957893 absolute error = 7e-32 relative error = 1.9423612077247453220752734249901e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.83 y[1] (analytic) = -0.350518618171241462912859316174 y[1] (numeric) = -0.35051861817124146291285931617439 absolute error = 3.9e-31 relative error = 1.1126370463136722868689501502026e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.625 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.84 y[1] (analytic) = -0.340647399102754948501802482783 y[1] (numeric) = -0.34064739910275494850180248278258 absolute error = 4.2e-31 relative error = 1.2329464458153947374034072942092e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.85 y[1] (analytic) = -0.330772454251767928282440020258 y[1] (numeric) = -0.330772454251767928282440020258 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.86 y[1] (analytic) = -0.320893785005908958235079555837 y[1] (numeric) = -0.32089378500590895823507955583663 absolute error = 3.7e-31 relative error = 1.1530294985089436894189020418031e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.87 y[1] (analytic) = -0.311011392751773363772505050017 y[1] (numeric) = -0.31101139275177336377250505001703 absolute error = 3e-32 relative error = 9.6459488942078126611636052928300e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.88 y[1] (analytic) = -0.301125278874924393328361219946 y[1] (numeric) = -0.30112527887492439332836121994652 absolute error = 5.2e-31 relative error = 1.7268560180096589103936653267018e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.72 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.89 y[1] (analytic) = -0.291235444759894370228888383088 y[1] (numeric) = -0.29123544475989437022888838308813 absolute error = 1.3e-31 relative error = 4.4637423891579188703654134608590e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.9 y[1] (analytic) = -0.281341891790185842851199706697 y[1] (numeric) = -0.28134189179018584285119970669697 absolute error = 3e-32 relative error = 1.0663182723734887997782015817180e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=72032200, alloc=4455632, time=2.86 TOP MAIN SOLVE Loop x[1] = 24.91 y[1] (analytic) = -0.271444621348272733071285728963 y[1] (numeric) = -0.27144462134827273307128572896334 absolute error = 3.4e-31 relative error = 1.2525575136144192424595218882409e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.92 y[1] (analytic) = -0.261543634815601483004923916528 y[1] (numeric) = -0.26154363481560148300492391652845 absolute error = 4.5e-31 relative error = 1.7205542024269397469266404625254e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.93 y[1] (analytic) = -0.251638933572592200044663940392 y[1] (numeric) = -0.25163893357259220004466394039251 absolute error = 5.1e-31 relative error = 2.0267134054312641371917576529083e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.94 y[1] (analytic) = -0.241730518998639800196052287959 y[1] (numeric) = -0.24173051899863980019605228795884 absolute error = 1.6e-31 relative error = 6.6189408214897477715990501927506e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.95 y[1] (analytic) = -0.231818392472115149716252783038 y[1] (numeric) = -0.23181839247211514971625278303751 absolute error = 4.9e-31 relative error = 2.1137235694486185571979690586143e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.96 y[1] (analytic) = -0.221902555370366205058212558012 y[1] (numeric) = -0.22190255537036620505821255801239 absolute error = 3.9e-31 relative error = 1.7575282057886667782589625463729e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 24.97 y[1] (analytic) = -0.211983009069719151123516013003 y[1] (numeric) = -0.2119830090697191511235160130033 absolute error = 3.0e-31 relative error = 1.4152077627190060129763542925718e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.98 y[1] (analytic) = -0.202059754945479537827062305675 y[1] (numeric) = -0.20205975494547953782706230567493 absolute error = 7e-32 relative error = 3.4643217309101281543421235960497e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.71 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 24.99 y[1] (analytic) = -0.192132794371933414976694942303 y[1] (numeric) = -0.19213279437193341497669494230317 absolute error = 1.7e-31 relative error = 8.8480470268345530510269490496194e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 86.83 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25 y[1] (analytic) = -0.182202128722348465470905085753 y[1] (numeric) = -0.1822021287223484654709050857533 absolute error = 3.0e-31 relative error = 1.6465230242022015248088969247791e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.01 y[1] (analytic) = -0.1722677593689751368177232591 y[1] (numeric) = -0.17226775936897513681772325909966 absolute error = 3.4e-31 relative error = 1.9736716913567338949848522655508e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 19.44 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.02 y[1] (analytic) = -0.16232968768304777097790720467 y[1] (numeric) = -0.16232968768304777097790720466972 absolute error = 2.8e-31 relative error = 1.7248847330175738459874169907369e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 27.66 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.03 y[1] (analytic) = -0.152387915034785732535526757273 y[1] (numeric) = -0.15238791503478573253552675727323 absolute error = 2.3e-31 relative error = 1.5093060361610543979937351698530e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 55.83 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.04 y[1] (analytic) = -0.142442442793394535199039707227 y[1] (numeric) = -0.14244244279339453519903970722686 absolute error = 1.4e-31 relative error = 9.8285312477449454215770974119138e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.26 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.05 y[1] (analytic) = -0.132493272327066966635945763453 y[1] (numeric) = -0.13249327232706696663594576345304 absolute error = 4e-32 relative error = 3.0190212149985841469810303824193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.06 y[1] (analytic) = -0.122540405002984211644098879366 y[1] (numeric) = -0.12254040500298421164409887936628 absolute error = 2.8e-31 relative error = 2.2849606217082536483080075901023e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.07 y[1] (analytic) = -0.112583842187316973662751374408 y[1] (numeric) = -0.11258384218731697366275137440843 absolute error = 4.3e-31 relative error = 3.8193757793819657329278016729276e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.08 y[1] (analytic) = -0.102623585245226594626396471904 y[1] (numeric) = -0.10262358524522659462639647190348 absolute error = 5.2e-31 relative error = 5.0670613266669821181782459164221e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.09 y[1] (analytic) = -0.092659635540866173164469079321 y[1] (numeric) = -0.092659635540866173164469079321142 absolute error = 1.42e-31 relative error = 1.5324903791292486013893423482325e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.1 y[1] (analytic) = -0.082691994437381681149957860014 y[1] (numeric) = -0.082691994437381681149957860013719 absolute error = 2.81e-31 relative error = 3.3981524077616315200893631295355e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.11 y[1] (analytic) = -0.072720663296913078599974885972 y[1] (numeric) = -0.072720663296913078599974885971654 absolute error = 3.46e-31 relative error = 4.7579323993141762685670630687758e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.12 y[1] (analytic) = -0.062745643480595426931322419077 y[1] (numeric) = -0.062745643480595426931322419077262 absolute error = 2.62e-31 relative error = 4.1755887017243757499650984706766e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 28.15 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.13 y[1] (analytic) = -0.052766936348560000574089643673 y[1] (numeric) = -0.052766936348560000574089643672629 absolute error = 3.71e-31 relative error = 7.0309179511446947556823844138419e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.14 y[1] (analytic) = -0.042784543259935396946305465945 y[1] (numeric) = -0.042784543259935396946305465944746 absolute error = 2.54e-31 relative error = 5.9367234203444791071469325825067e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.54 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.15 y[1] (analytic) = -0.032798465572848644792666805618 y[1] (numeric) = -0.032798465572848644792666805617746 absolute error = 2.54e-31 relative error = 7.7442647259165466079907409172130e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 42.42 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.16 y[1] (analytic) = -0.022808704644426310890355132678 y[1] (numeric) = -0.022808704644426310890355132677524 absolute error = 4.76e-31 relative error = 2.0869225474245358986334394878480e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.42 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.17 y[1] (analytic) = -0.012815261830795605124947346287 y[1] (numeric) = -0.012815261830795605124947346287318 absolute error = 3.18e-31 relative error = 2.4814163315480049344799351535338e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.18 y[1] (analytic) = -0.002818138487085483939420454633 y[1] (numeric) = -0.0028181384870854839394204546332971 absolute error = 2.971e-31 relative error = 1.0542420160027711368357324976188e-26 % Correct digits = 28 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.68 Order of pole (six term test) = -0.5 bytes used=76032876, alloc=4455632, time=3.02 TOP MAIN SOLVE Loop x[1] = 25.19 y[1] (analytic) = 0.007182664032572247840757106883 y[1] (numeric) = 0.0071826640325722478407571068835399 absolute error = 5.399e-31 relative error = 7.5167096435478355305706756704826e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 57.82 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.2 y[1] (analytic) = 0.017187144375041836803461285969 y[1] (numeric) = 0.017187144375041836803461285969198 absolute error = 1.98e-31 relative error = 1.1520238364176656894565172617942e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.21 y[1] (analytic) = 0.027195301188182482363695706411 y[1] (numeric) = 0.027195301188182482363695706412314 absolute error = 1.314e-30 relative error = 4.8317170341580515852052651484116e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.22 y[1] (analytic) = 0.037207133120847239792349368186 y[1] (numeric) = 0.037207133120847239792349368187321 absolute error = 1.321e-30 relative error = 3.5503944786862408097063170349557e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.23 y[1] (analytic) = 0.047222638822881924856962232597 y[1] (numeric) = 0.04722263882288192485696223259609 absolute error = 9.10e-31 relative error = 1.9270418229128181166336129093702e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.24 y[1] (analytic) = 0.05724181694512402007153870695 y[1] (numeric) = 0.057241816945124020071538706949233 absolute error = 7.67e-31 relative error = 1.3399295147030351107547238724284e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.25 y[1] (analytic) = 0.067264666139401582552455563082 y[1] (numeric) = 0.067264666139401582552455563081154 absolute error = 8.46e-31 relative error = 1.2577182770025511132501081304277e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.26 y[1] (analytic) = 0.077291185058532153477517327039 y[1] (numeric) = 0.077291185058532153477517327037711 absolute error = 1.289e-30 relative error = 1.6677192865186993673867439775612e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.27 y[1] (analytic) = 0.087321372356321669145218663622 y[1] (numeric) = 0.087321372356321669145218663621164 absolute error = 8.36e-31 relative error = 9.5738302942449966251281858759718e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.28 y[1] (analytic) = 0.097355226687563373631279749172 y[1] (numeric) = 0.097355226687563373631279749172993 absolute error = 9.93e-31 relative error = 1.0199760544821889988433095075640e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.29 y[1] (analytic) = 0.10739274670803673303952707907 y[1] (numeric) = 0.1073927467080367330395270790699 absolute error = 1.0e-31 relative error = 9.3116158274510826849737385738996e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.3 y[1] (analytic) = 0.117433931074506351344198592951 y[1] (numeric) = 0.11743393107450635134419859295062 absolute error = 3.8e-31 relative error = 3.2358620419417597951458455505954e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.31 y[1] (analytic) = 0.127478778444720887820758420728 y[1] (numeric) = 0.12747877844472088782075842072944 absolute error = 1.44e-30 relative error = 1.1295997793267471018248718631178e-27 % Correct digits = 29 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.32 y[1] (analytic) = 0.137527287477411976062312956035 y[1] (numeric) = 0.13752728747741197606231295603512 absolute error = 1.2e-31 relative error = 8.7255411054122094232268142208632e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.33 y[1] (analytic) = 0.147579456832293144578726350889 y[1] (numeric) = 0.14757945683229314457872635088916 absolute error = 1.6e-31 relative error = 1.0841617352056076163730837017686e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.34 y[1] (analytic) = 0.157635285170058738975539896254 y[1] (numeric) = 0.15763528517005873897553989625326 absolute error = 7.4e-31 relative error = 4.6943804440844547044626630144511e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.35 y[1] (analytic) = 0.167694771152382845709806107581 y[1] (numeric) = 0.16769477115238284570980610758012 absolute error = 8.8e-31 relative error = 5.2476293324635107977753224961497e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.36 y[1] (analytic) = 0.177757913441918217419954672742 y[1] (numeric) = 0.17775791344191821741995467274246 absolute error = 4.6e-31 relative error = 2.5877891515097211515198596211331e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.37 y[1] (analytic) = 0.187824710702295199826813741739 y[1] (numeric) = 0.18782471070229519982681374173918 absolute error = 1.8e-31 relative error = 9.5834035536092225900256366808615e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.38 y[1] (analytic) = 0.197895161598120660202916343434 y[1] (numeric) = 0.1978951615981206602029163434332 absolute error = 8.0e-31 relative error = 4.0425445146790153498523862324674e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 29.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.39 y[1] (analytic) = 0.207969264794976917407228004308 y[1] (numeric) = 0.20796926479497691740722800430926 absolute error = 1.26e-30 relative error = 6.0585875573592583364085455743436e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.4 y[1] (analytic) = 0.218047018959420673482437917899 y[1] (numeric) = 0.21804701895942067348243791789915 absolute error = 1.5e-31 relative error = 6.8792502055676135626863775903746e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.41 y[1] (analytic) = 0.228128422758981946811962271154 y[1] (numeric) = 0.22812842275898194681196227115371 absolute error = 2.9e-31 relative error = 1.2712138035793351191686094194378e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 22.82 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.42 y[1] (analytic) = 0.238213474862163006833814575692 y[1] (numeric) = 0.23821347486216300683381457569154 absolute error = 4.6e-31 relative error = 1.9310410557848118911402245542876e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.43 y[1] (analytic) = 0.248302173938437310308504077571 y[1] (numeric) = 0.24830217393843731030850407757123 absolute error = 2.3e-31 relative error = 9.2629072211435792056189526727273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.44 y[1] (analytic) = 0.258394518658248439138129529063 y[1] (numeric) = 0.25839451865824843913812952906276 absolute error = 2.4e-31 relative error = 9.2881227220389703302236964078640e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.45 y[1] (analytic) = 0.268490507693009039733841799882 y[1] (numeric) = 0.26849050769300903973384179988122 absolute error = 7.8e-31 relative error = 2.9051306383309790763994696088460e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.89 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.46 y[1] (analytic) = 0.278590139715099763928854983539 y[1] (numeric) = 0.27859013971509976392885498353836 absolute error = 6.4e-31 relative error = 2.2972815931478984439640698926009e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.47 y[1] (analytic) = 0.28869341339786821143419181691 y[1] (numeric) = 0.28869341339786821143419181691057 absolute error = 5.7e-31 relative error = 1.9744129015317847596160973475617e-28 % Correct digits = 30 h = 0.01 bytes used=80034284, alloc=4455632, time=3.18 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.48 y[1] (analytic) = 0.298800327415627873834355377862 y[1] (numeric) = 0.29880032741562787383435537786146 absolute error = 5.4e-31 relative error = 1.8072269353603020364834462293071e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.49 y[1] (analytic) = 0.30891088044365708012012515684 y[1] (numeric) = 0.30891088044365708012012515683954 absolute error = 4.6e-31 relative error = 1.4891026154188841831793563930296e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.5 y[1] (analytic) = 0.319025071158197943755681713842 y[1] (numeric) = 0.31902507115819794375568171384132 absolute error = 6.8e-31 relative error = 2.1314939215633057393189976221928e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.51 y[1] (analytic) = 0.329142898236455311277270232033 y[1] (numeric) = 0.32914289823645531127727023203361 absolute error = 6.1e-31 relative error = 1.8532983797261752089579847910080e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.52 y[1] (analytic) = 0.33926436035659571242061936371 y[1] (numeric) = 0.33926436035659571242061936371069 absolute error = 6.9e-31 relative error = 2.0338122143886592876431777186253e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.53 y[1] (analytic) = 0.349389456197746311774337833167 y[1] (numeric) = 0.34938945619774631177433783316788 absolute error = 8.8e-31 relative error = 2.5186793258636301055638941946904e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 26.29 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.54 y[1] (analytic) = 0.359518184439993861956517314547 y[1] (numeric) = 0.35951818443999386195651731454732 absolute error = 3.2e-31 relative error = 8.9008015129596392481902279232964e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.55 y[1] (analytic) = 0.369650543764383658311776140801 y[1] (numeric) = 0.36965054376438365831177614079977 absolute error = 1.23e-30 relative error = 3.3274670381223775788912252262040e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.56 y[1] (analytic) = 0.379786532852918495125984422651 y[1] (numeric) = 0.37978653285291849512598442265245 absolute error = 1.45e-30 relative error = 3.8179342198043328475757771072437e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.57 y[1] (analytic) = 0.389926150388557623355917163922 y[1] (numeric) = 0.38992615038855762335591716392177 absolute error = 2.3e-31 relative error = 5.8985528354742874490690213896271e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.58 y[1] (analytic) = 0.400069395055215709871087951706 y[1] (numeric) = 0.40006939505521570987108795170597 absolute error = 3e-32 relative error = 7.4986990684102541955953963930652e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.59 y[1] (analytic) = 0.41021626553776179820502177698 y[1] (numeric) = 0.41021626553776179820502177697993 absolute error = 7e-32 relative error = 1.7064169775968150303351779315669e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.6 y[1] (analytic) = 0.420366760522018270813231502936 y[1] (numeric) = 0.42036676052201827081323150293754 absolute error = 1.54e-30 relative error = 3.6634675826594923616695158058634e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.61 y[1] (analytic) = 0.430520878694759812835168445129 y[1] (numeric) = 0.43052087869475981283516844512918 absolute error = 1.8e-31 relative error = 4.1809818967600028910555943641395e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 61.64 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.62 y[1] (analytic) = 0.440678618743712377357423459068 y[1] (numeric) = 0.44067861874371237735742345906747 absolute error = 5.3e-31 relative error = 1.2026905265132336629538755211252e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 72.94 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.63 y[1] (analytic) = 0.450839979357552152175460847568 y[1] (numeric) = 0.45083997935755215217546084756706 absolute error = 9.4e-31 relative error = 2.0849969901504782895315021400979e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.64 y[1] (analytic) = 0.461004959225904528051173301687 y[1] (numeric) = 0.46100495922590452805117330168698 absolute error = 2e-32 relative error = 4.3383481239731035399386299502772e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.65 y[1] (analytic) = 0.471173557039343068463551975801 y[1] (numeric) = 0.47117355703934306846355197580099 absolute error = 1e-32 relative error = 2.1223601899129917380824832505820e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.36 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.66 y[1] (analytic) = 0.481345771489388480849771669074 y[1] (numeric) = 0.48134577148938848084977166907507 absolute error = 1.07e-30 relative error = 2.2229342468080426657071026866934e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.67 y[1] (analytic) = 0.491521601268507589333996942526 y[1] (numeric) = 0.49152160126850758933399694252529 absolute error = 7.1e-31 relative error = 1.4444939920598574067237504119206e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.68 y[1] (analytic) = 0.501701045070112308941220842906 y[1] (numeric) = 0.50170104507011230894122084290634 absolute error = 3.4e-31 relative error = 6.7769442248717117837144870353465e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.69 y[1] (analytic) = 0.511884101588558621293453731985 y[1] (numeric) = 0.51188410158855862129345373198418 absolute error = 8.2e-31 relative error = 1.6019251183133995422727786875497e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.7 y[1] (analytic) = 0.522070769519145551785585532318 y[1] (numeric) = 0.52207076951914555178558553231794 absolute error = 6e-32 relative error = 1.1492694765359710523333327310172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.71 y[1] (analytic) = 0.53226104755811414823825049856 y[1] (numeric) = 0.53226104755811414823825049855912 absolute error = 8.8e-31 relative error = 1.6533240672734340569391458491759e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.72 y[1] (analytic) = 0.542454934402646461025029406512 y[1] (numeric) = 0.54245493440264646102502940651273 absolute error = 7.3e-31 relative error = 1.3457339102351035184103624896647e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.73 y[1] (analytic) = 0.552652428750864524671329820838 y[1] (numeric) = 0.55265242875086452467132982083733 absolute error = 6.7e-31 relative error = 1.2123352131363485051875323546463e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.74 y[1] (analytic) = 0.562853529301829340922290856332 y[1] (numeric) = 0.56285352930182934092229085633125 absolute error = 7.5e-31 relative error = 1.3324958642976077911334810607209e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.75 y[1] (analytic) = 0.573058234755539863277064587304 y[1] (numeric) = 0.57305823475553986327706458730283 absolute error = 1.17e-30 relative error = 2.0416773183603385725544708369711e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=84035520, alloc=4521156, time=3.34 x[1] = 25.76 y[1] (analytic) = 0.583266543812931982986831984595 y[1] (numeric) = 0.58326654381293198298683198459454 absolute error = 4.6e-31 relative error = 7.8866172743748762906228067832902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.77 y[1] (analytic) = 0.593478455175877516513916970467 y[1] (numeric) = 0.59347845517587751651391697046676 absolute error = 2.4e-31 relative error = 4.0439547199548453481089034809621e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.87 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.78 y[1] (analytic) = 0.603693967547183194449367877787 y[1] (numeric) = 0.60369396754718319444936787778794 absolute error = 9.4e-31 relative error = 1.5570803263435491861012295543781e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.79 y[1] (analytic) = 0.613913079630589651886381281864 y[1] (numeric) = 0.61391307963058965188638128186542 absolute error = 1.42e-30 relative error = 2.3130310252624974145196899556953e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.7 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.8 y[1] (analytic) = 0.624135790130770420246948840827 y[1] (numeric) = 0.62413579013077042024694884082676 absolute error = 2.4e-31 relative error = 3.8453170575222841689707461735161e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.81 y[1] (analytic) = 0.634362097753330920559113433765 y[1] (numeric) = 0.63436209775333092055911343376599 absolute error = 9.9e-31 relative error = 1.5606228737596447756635714137193e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.82 y[1] (analytic) = 0.644592001204807458182226524945 y[1] (numeric) = 0.64459200120480745818222652494415 absolute error = 8.5e-31 relative error = 1.3186635862859983934167770182302e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 125.7 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.83 y[1] (analytic) = 0.65482549919266621897760430722 y[1] (numeric) = 0.65482549919266621897760430721927 absolute error = 7.3e-31 relative error = 1.1148008147208933629424419711198e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.84 y[1] (analytic) = 0.665062590425302266921985788618 y[1] (numeric) = 0.6650625904253022669219857886188 absolute error = 8.0e-31 relative error = 1.2028943012542719126767001920713e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.85 y[1] (analytic) = 0.675303273612038543161201582599 y[1] (numeric) = 0.67530327361203854316120158259785 absolute error = 1.15e-30 relative error = 1.7029385832070977544942644286560e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.07 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.86 y[1] (analytic) = 0.68554754746312486650146774509 y[1] (numeric) = 0.68554754746312486650146774509005 absolute error = 5e-32 relative error = 7.2934401392033957772953434597293e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.87 y[1] (analytic) = 0.695795410689736935335724569994 y[1] (numeric) = 0.69579541068973693533572456999454 absolute error = 5.4e-31 relative error = 7.7609020080299455173763714555352e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 25.16 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.88 y[1] (analytic) = 0.706046862003975331002445809294 y[1] (numeric) = 0.70604686200397533100244580929337 absolute error = 6.3e-31 relative error = 8.9229204731803318143075435076792e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.89 y[1] (analytic) = 0.716301900118864522574349324597 y[1] (numeric) = 0.7163019001188645225743493245979 absolute error = 9.0e-31 relative error = 1.2564534588706972011025584629808e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.9 y[1] (analytic) = 0.726560523748351873074445703622 y[1] (numeric) = 0.72656052374835187307444570362115 absolute error = 8.5e-31 relative error = 1.1698956552371155941562883134750e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.91 y[1] (analytic) = 0.736822731607306647116866887905 y[1] (numeric) = 0.73682273160730664711686688790497 absolute error = 3e-32 relative error = 4.0715356235763705718641198411264e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.09 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.92 y[1] (analytic) = 0.747088522411519019969922357137 y[1] (numeric) = 0.74708852241151901996992235713652 absolute error = 4.8e-31 relative error = 6.4249414306434952819385410742110e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.93 y[1] (analytic) = 0.757357894877699088038835900606 y[1] (numeric) = 0.75735789487769908803883590060701 absolute error = 1.01e-30 relative error = 1.3335835102941634740406933560740e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.94 y[1] (analytic) = 0.767630847723475880765621477837 y[1] (numeric) = 0.76763084772347588076562147783694 absolute error = 6e-32 relative error = 7.8162570170204827247134286074203e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.95 y[1] (analytic) = 0.777907379667396373943562128156 y[1] (numeric) = 0.77790737966739637394356212815506 absolute error = 9.4e-31 relative error = 1.2083700766560516100437285424264e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.96 y[1] (analytic) = 0.788187489428924504443761333113 y[1] (numeric) = 0.78818748942892450444376133311265 absolute error = 3.5e-31 relative error = 4.4405678178625995029900428594547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.97 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.97 y[1] (analytic) = 0.798471175728440186351241666078 y[1] (numeric) = 0.79847117572844018635124166607934 absolute error = 1.34e-30 relative error = 1.6782071046929483759028507856813e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.98 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 25.98 y[1] (analytic) = 0.808758437287238328508070980239 y[1] (numeric) = 0.80875843728723832850807098024042 absolute error = 1.42e-30 relative error = 1.7557776642961603607676069562568e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 25.99 y[1] (analytic) = 0.819049272827527853461001789537 y[1] (numeric) = 0.81904927282752785346100178953768 absolute error = 6.8e-31 relative error = 8.3023088177894237909100671319702e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 25.82 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26 y[1] (analytic) = 0.829343681072430717811114886906 y[1] (numeric) = 0.8293436810724307178111148869047 absolute error = 1.30e-30 relative error = 1.5675045577232347896937939466386e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 18.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.01 y[1] (analytic) = 0.839641660745980933962963620481 y[1] (numeric) = 0.83964166074598093396296362048175 absolute error = 7.5e-31 relative error = 8.9323819322359652612719490517607e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.02 y[1] (analytic) = 0.849943210573123593270720611394 y[1] (numeric) = 0.84994321057312359327072061139382 absolute error = 1.8e-31 relative error = 2.1177885505859214006787647146561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.03 y[1] (analytic) = 0.860248329279713890578834046175 y[1] (numeric) = 0.86024832927971389057883404617592 absolute error = 9.2e-31 relative error = 1.0694586303588827612697469599664e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.59 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.04 y[1] (analytic) = 0.870557015592516150154706013072 bytes used=88037084, alloc=4521156, time=3.51 y[1] (numeric) = 0.87055701559251615015470601307094 absolute error = 1.06e-30 relative error = 1.2176112316762454445583454675980e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.9 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.05 y[1] (analytic) = 0.880869268239202853010910674246 y[1] (numeric) = 0.88086926823920285301091067424522 absolute error = 7.8e-31 relative error = 8.8548894611701735265803925850456e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.06 y[1] (analytic) = 0.891185085948353665614475375504 y[1] (numeric) = 0.89118508594835366561447537550349 absolute error = 5.1e-31 relative error = 5.7227169534293096926562804691551e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.67 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.07 y[1] (analytic) = 0.901504467449454469980753091375 y[1] (numeric) = 0.90150446744945446998075309137597 absolute error = 9.7e-31 relative error = 1.0759791382335949830794039790835e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.08 y[1] (analytic) = 0.911827411472896395149419886533 y[1] (numeric) = 0.91182741147289639514941988653364 absolute error = 6.4e-31 relative error = 7.0188721236861354617623722131557e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.09 y[1] (analytic) = 0.9221539167499748500401363444 y[1] (numeric) = 0.92215391674997485004013634440107 absolute error = 1.07e-30 relative error = 1.1603269048306942325580977495654e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.647 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.1 y[1] (analytic) = 0.932483982012888557685417170616 y[1] (numeric) = 0.93248398201288855768541717061684 absolute error = 8.4e-31 relative error = 9.0081976334515709945563665309449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 35.25 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.11 y[1] (analytic) = 0.942817605994738590838258422678 y[1] (numeric) = 0.94281760599473859083825842267713 absolute error = 8.7e-31 relative error = 9.2276596710568326967949426362852e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.12 y[1] (analytic) = 0.953154787429527408952077047727 y[1] (numeric) = 0.9531547874295274089520770477256 absolute error = 1.40e-30 relative error = 1.4688065553083219483915688751798e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.13 y[1] (analytic) = 0.96349552505215789653052262806 y[1] (numeric) = 0.9634955250521578965305226280595 absolute error = 5.0e-31 relative error = 5.1894376984566999887957984605505e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.14 y[1] (analytic) = 0.973839817598432402844726438545 y[1] (numeric) = 0.97383981759843240284472643854515 absolute error = 1.5e-31 relative error = 1.5402943819848330681888553667854e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.73 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.15 y[1] (analytic) = 0.984187663805051783015558111811 y[1] (numeric) = 0.98418766380505178301555811181201 absolute error = 1.01e-30 relative error = 1.0262270470807904101606469538817e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.16 y[1] (analytic) = 0.99453906240961444045846538586 y[1] (numeric) = 0.99453906240961444045846538586095 absolute error = 9.5e-31 relative error = 9.5521637702022163329578642747297e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.17 y[1] (analytic) = 1.004894012150615370688477574616 y[1] (numeric) = 1.0048940121506153706884775746151 absolute error = 9e-31 relative error = 8.9561684030126983939394916174899e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 128.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.18 y[1] (analytic) = 1.015252511767445206482958554998 y[1] (numeric) = 1.0152525117674452064829585549977 absolute error = 3e-31 relative error = 2.9549298969744219771486950558776e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 161.3 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.19 y[1] (analytic) = 1.025614560000389264399700204379 y[1] (numeric) = 1.0256145600003892643997002043775 absolute error = 1.5e-30 relative error = 1.4625377393232704166415728664626e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.2 y[1] (analytic) = 1.035980155590626592647952349712 y[1] (numeric) = 1.035980155590626592647952349713 absolute error = 1.0e-30 relative error = 9.6526945482839503900299951394597e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.21 y[1] (analytic) = 1.046349297280229020309990404493 y[1] (numeric) = 1.0463492972802290203099904044919 absolute error = 1.1e-30 relative error = 1.0512741804856418480733404195154e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.22 y[1] (analytic) = 1.056721983812160207910826971634 y[1] (numeric) = 1.0567219838121602079108269716336 absolute error = 4e-31 relative error = 3.7852907967049810484969751221734e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.23 y[1] (analytic) = 1.067098213930274699333678779937 y[1] (numeric) = 1.0670982139302746993336787799384 absolute error = 1.4e-30 relative error = 1.3119692093229175319236324258619e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.24 y[1] (analytic) = 1.077477986379316975078805398465 y[1] (numeric) = 1.0774779863793169750788053984656 absolute error = 6e-31 relative error = 5.5685592428314827329215049085710e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.25 y[1] (analytic) = 1.087861299904920506863341237432 y[1] (numeric) = 1.0878612999049205068633412374323 absolute error = 3e-31 relative error = 2.7577044980478680010908332372023e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.26 y[1] (analytic) = 1.098248153253606813559747395891 y[1] (numeric) = 1.098248153253606813559747395891 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.27 y[1] (analytic) = 1.108638545172784518470514955594 y[1] (numeric) = 1.1086385451727845184705149555939 absolute error = 1e-31 relative error = 9.0200724515143672231745583952160e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.28 y[1] (analytic) = 1.119032474410748407936756347125 y[1] (numeric) = 1.1190324744107484079367563471254 absolute error = 4e-31 relative error = 3.5745164608438101989922019924825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.29 y[1] (analytic) = 1.129429939716678491278326428614 y[1] (numeric) = 1.1294299397166784912783264286149 absolute error = 9e-31 relative error = 7.9686217652931017048965492852190e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 30.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.3 y[1] (analytic) = 1.139830939840639062063119919167 y[1] (numeric) = 1.1398309398406390620631199191674 absolute error = 4e-31 relative error = 3.5092923522143065538680604860918e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.31 y[1] (analytic) = 1.1502354735335777607031968186 y[1] (numeric) = 1.1502354735335777607031968185997 absolute error = 3e-31 relative error = 2.6081616060612860012932027257463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.32 y[1] (analytic) = 1.160643539547324638375392422185 y[1] (numeric) = 1.1606435395473246383753924221864 absolute error = 1.4e-30 relative error = 1.2062273663678250509816762667194e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=92038652, alloc=4521156, time=3.67 TOP MAIN SOLVE Loop x[1] = 26.33 y[1] (analytic) = 1.171055136634591222264073503933 y[1] (numeric) = 1.1710551366345912222640735039319 absolute error = 1.1e-30 relative error = 9.3932383334332888361704093341581e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 71.27 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.34 y[1] (analytic) = 1.18147026354896958212370719443 y[1] (numeric) = 1.18147026354896958212370719443 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.74 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.35 y[1] (analytic) = 1.191888919044931398158914019686 y[1] (numeric) = 1.1918889190449313981589140196858 absolute error = 2e-31 relative error = 1.6780087204792653350156838463277e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.36 y[1] (analytic) = 1.202311101877827030219681495388 y[1] (numeric) = 1.202311101877827030219681495388 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.37 y[1] (analytic) = 1.212736810803884588309419587072 y[1] (numeric) = 1.2127368108038845883094195870705 absolute error = 1.5e-30 relative error = 1.2368718312472908257367513377869e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.38 y[1] (analytic) = 1.223166044580209004403544250423 y[1] (numeric) = 1.223166044580209004403544250423 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.62 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.39 y[1] (analytic) = 1.233598801964781105576280157735 y[1] (numeric) = 1.233598801964781105576280157735 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.4 y[1] (analytic) = 1.244035081716456688433378596124 y[1] (numeric) = 1.2440350817164566884333785961227 absolute error = 1.3e-30 relative error = 1.0449866077782354399168069515121e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.41 y[1] (analytic) = 1.254474882594965594848451390824 y[1] (numeric) = 1.2544748825949655948484513908236 absolute error = 4e-31 relative error = 3.1885851645955088408230765955867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.72 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.42 y[1] (analytic) = 1.26491820336091078900062656249 y[1] (numeric) = 1.2649182033609107890006265624883 absolute error = 1.7e-30 relative error = 1.3439604201149678485500405182191e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.43 y[1] (analytic) = 1.27536504277576743571123627108 y[1] (numeric) = 1.2753650427757674357112362710804 absolute error = 4e-31 relative error = 3.1363569376922881197893990988737e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.07 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.44 y[1] (analytic) = 1.285815399601881980077252430755 y[1] (numeric) = 1.2858153996018819800772524307556 absolute error = 6e-31 relative error = 4.6662996895648768810637206956634e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.45 y[1] (analytic) = 1.296269272602471228399190199952 y[1] (numeric) = 1.2962692726024712283991901999532 absolute error = 1.2e-30 relative error = 9.2573358434301615557425456652433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.46 y[1] (analytic) = 1.306726660541621430401204358941 y[1] (numeric) = 1.3067266605416214304012043589408 absolute error = 2e-31 relative error = 1.5305419720839136072962883616972e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.52 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.47 y[1] (analytic) = 1.317187562184287362741108383233 y[1] (numeric) = 1.3171875621842873627411083832326 absolute error = 4e-31 relative error = 3.0367732848667463047978998928421e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.48 y[1] (analytic) = 1.327651976296291413808050805688 y[1] (numeric) = 1.3276519762962914138080508056895 absolute error = 1.5e-30 relative error = 1.1298141582137379093709862395433e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.49 y[1] (analytic) = 1.338119901644322669805588232737 y[1] (numeric) = 1.338119901644322669805588232736 absolute error = 1.0e-30 relative error = 7.4731718642788991391675106931882e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.5 y[1] (analytic) = 1.348591336995936002117899141032 y[1] (numeric) = 1.3485913369959360021178991410334 absolute error = 1.4e-30 relative error = 1.0381202678630427229045453834402e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.51 y[1] (analytic) = 1.359066281119551155956887330154 y[1] (numeric) = 1.3590662811195511559568873301545 absolute error = 5e-31 relative error = 3.6789964326693288947201221332179e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 70.71 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.52 y[1] (analytic) = 1.369544732784451840287928644355 y[1] (numeric) = 1.369544732784451840287928644355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.53 y[1] (analytic) = 1.380026690760784819032019302455 y[1] (numeric) = 1.380026690760784819032019302454 absolute error = 1.0e-30 relative error = 7.2462366611816566772775456649627e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.54 y[1] (analytic) = 1.390512153819559003542088889163 y[1] (numeric) = 1.3905121538195590035420888891638 absolute error = 8e-31 relative error = 5.7532758545295871093037269108047e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.55 y[1] (analytic) = 1.401001120732644546351245763968 y[1] (numeric) = 1.4010011207326445463512457639683 absolute error = 3e-31 relative error = 2.1413259101685580736397900463077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.56 y[1] (analytic) = 1.411493590272771936190727334882 y[1] (numeric) = 1.4114935902727719361907273348813 absolute error = 7e-31 relative error = 4.9592857156703389869546518799876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.57 y[1] (analytic) = 1.421989561213531094275332324149 y[1] (numeric) = 1.4219895612135310942753323241499 absolute error = 9e-31 relative error = 6.3291603859028100537188742081017e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.58 y[1] (analytic) = 1.432489032329370471854116821234 y[1] (numeric) = 1.4324890323293704718541168212343 absolute error = 3e-31 relative error = 2.0942568719857490859241197289205e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.59 y[1] (analytic) = 1.44299200239559614902414057523 y[1] (numeric) = 1.4429920023955961490241405752301 absolute error = 1e-31 relative error = 6.9300453387117947112799853969617e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.6 y[1] (analytic) = 1.453498470188370934805054624329 y[1] (numeric) = 1.453498470188370934805054624329 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.61 y[1] (analytic) = 1.464008434484713468472325993977 y[1] (numeric) = 1.4640084344847134684723259939772 absolute error = 2e-31 relative error = 1.3661123480507400857319462412338e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.33 bytes used=96040312, alloc=4521156, time=3.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 80.42 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.62 y[1] (analytic) = 1.474521894062497322146899818113 y[1] (numeric) = 1.4745218940624973221468998181131 absolute error = 1e-31 relative error = 6.7818592862319017932692837800198e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.63 y[1] (analytic) = 1.485038847700450104639103849285 y[1] (numeric) = 1.4850388477004501046391038492838 absolute error = 1.2e-30 relative error = 8.0805966918520247986791235952580e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.64 y[1] (analytic) = 1.495559294178152566544604923581 y[1] (numeric) = 1.495559294178152566544604923581 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.65 y[1] (analytic) = 1.506083232276037706590231535238 y[1] (numeric) = 1.5060832322760377065902315352373 absolute error = 7e-31 relative error = 4.6478174977231451689640445630212e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.66 y[1] (analytic) = 1.516610660775389879227481253408 y[1] (numeric) = 1.5166106607753898792274812534088 absolute error = 8e-31 relative error = 5.2749200614941479908781826727561e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.67 y[1] (analytic) = 1.527141578458343903471536280179 y[1] (numeric) = 1.5271415784583439034715362801783 absolute error = 7e-31 relative error = 4.5837269436842460851289243709848e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.68 y[1] (analytic) = 1.537675984107884172983615004168 y[1] (numeric) = 1.5376759841078841729836150041678 absolute error = 2e-31 relative error = 1.3006641325417741100203589370608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.69 y[1] (analytic) = 1.548213876507843767394491948388 y[1] (numeric) = 1.5482138765078437673944919483888 absolute error = 8e-31 relative error = 5.1672447336829365605021287580195e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.7 y[1] (analytic) = 1.558755254442903564867023044112 y[1] (numeric) = 1.5587552544429035648670230441102 absolute error = 1.8e-30 relative error = 1.1547675588386817598483347684006e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 79.86 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.71 y[1] (analytic) = 1.569300116698591355895517684616 y[1] (numeric) = 1.5693001166985913558955176846163 absolute error = 3e-31 relative error = 1.9116802248834579960357416508022e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.72 y[1] (analytic) = 1.579848462061280958339803523798 y[1] (numeric) = 1.5798484620612809583398035237979 absolute error = 1e-31 relative error = 6.3297210081482540510882794292298e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.73 y[1] (analytic) = 1.590400289318191333691834484594 y[1] (numeric) = 1.5904002893181913336918344845926 absolute error = 1.4e-30 relative error = 8.8028153000411209428779408290785e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.74 y[1] (analytic) = 1.6009555972573857045726969314 y[1] (numeric) = 1.6009555972573857045726969314003 absolute error = 3e-31 relative error = 1.8738808278876268314322739677845e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 7.561 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.75 y[1] (analytic) = 1.611514384667770673457873438776 y[1] (numeric) = 1.6115143846677706734578734387752 absolute error = 8e-31 relative error = 4.9642746450875011097760538122891e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.98 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.76 y[1] (analytic) = 1.62207665033909534262862805597 y[1] (numeric) = 1.6220766503390953426286280559685 absolute error = 1.5e-30 relative error = 9.2474051684698426402796518644085e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.77 y[1] (analytic) = 1.632642393061950435347381423295 y[1] (numeric) = 1.6326423930619504353473814232944 absolute error = 6e-31 relative error = 3.6750240135240263006266955456077e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.78 y[1] (analytic) = 1.643211611627767418254948541851 y[1] (numeric) = 1.6432116116277674182549485418502 absolute error = 8e-31 relative error = 4.8685147691204483904131622166226e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.79 y[1] (analytic) = 1.653784304828817624987516432862 y[1] (numeric) = 1.6537843048288176249875164328625 absolute error = 5e-31 relative error = 3.0233688791220856732383543625926e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.8 y[1] (analytic) = 1.664360471458211381011243346895 y[1] (numeric) = 1.6643604714582113810112433468954 absolute error = 4e-31 relative error = 2.4033255226828617063640402271617e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.81 y[1] (analytic) = 1.674940110309897129672365596364 y[1] (numeric) = 1.674940110309897129672365596363 absolute error = 1.0e-30 relative error = 5.9703627242826023962384759172885e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.82 y[1] (analytic) = 1.685523220178660559460702487274 y[1] (numeric) = 1.6855232201786605594607024872752 absolute error = 1.2e-30 relative error = 7.1194510145805258610925438978530e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.83 y[1] (analytic) = 1.696109799860123732484454217937 y[1] (numeric) = 1.696109799860123732484454217938 absolute error = 1.0e-30 relative error = 5.8958447152564584867213957701394e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.84 y[1] (analytic) = 1.70669984815074421415419199346 y[1] (numeric) = 1.7066998481507442141541919934589 absolute error = 1.1e-30 relative error = 6.4451871908928800243451996729463e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.85 y[1] (analytic) = 1.717293363847814204073943975404 y[1] (numeric) = 1.7172933638478142040739439754031 absolute error = 9e-31 relative error = 5.2408052051365034631538447481074e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.86 y[1] (analytic) = 1.727890345749459668137285045838 y[1] (numeric) = 1.7278903457494596681372850458374 absolute error = 6e-31 relative error = 3.4724425741250057976164531010570e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.87 y[1] (analytic) = 1.738490792654639471826342714314 y[1] (numeric) = 1.7384907926546394718263427143152 absolute error = 1.2e-30 relative error = 6.9025387138670135113912155446600e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.88 y[1] (analytic) = 1.749094703363144514711635835124 y[1] (numeric) = 1.7490947033631445147116358351254 absolute error = 1.4e-30 relative error = 8.0041406409160797917474731382755e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.48 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.89 y[1] (analytic) = 1.759702076675596866150667130385 y[1] (numeric) = 1.7597020766755968661506671303838 absolute error = 1.2e-30 relative error = 6.8193361586923978044789711182382e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=100042808, alloc=4521156, time=3.99 x[1] = 26.9 y[1] (analytic) = 1.77031291139344890218319483231 y[1] (numeric) = 1.7703129113934489021831948323103 absolute error = 3e-31 relative error = 1.6946156697454348086806780462796e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.91 y[1] (analytic) = 1.780927206318982443621113065347 y[1] (numeric) = 1.780927206318982443621113065346 absolute error = 1.0e-30 relative error = 5.6150526335487385383282516198293e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.92 y[1] (analytic) = 1.791544960255307895330874885642 y[1] (numeric) = 1.7915449602553078953308748856415 absolute error = 5e-31 relative error = 2.7908872570451508223930054881586e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.93 y[1] (analytic) = 1.802166172006363386706396181928 y[1] (numeric) = 1.8021661720063633867063961819277 absolute error = 3e-31 relative error = 1.6646633626798578612357275044953e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.94 y[1] (analytic) = 1.812790840376913913330382917888 y[1] (numeric) = 1.8127908403769139133303829178871 absolute error = 9e-31 relative error = 4.9647205841622234454977230915857e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.95 y[1] (analytic) = 1.823418964172550479822028461908 y[1] (numeric) = 1.8234189641725504798220284619075 absolute error = 5e-31 relative error = 2.7421015675730621932889646732135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 30.68 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.96 y[1] (analytic) = 1.834050542199689243869032005549 y[1] (numeric) = 1.8340505421996892438690320055493 absolute error = 3e-31 relative error = 1.6357237333284807396071233975128e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.97 y[1] (analytic) = 1.844685573265570661441893317222 y[1] (numeric) = 1.8446855732655706614418933172222 absolute error = 2e-31 relative error = 1.0841956098022074436055834515975e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.76 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 26.98 y[1] (analytic) = 1.855324056178258633188443312471 y[1] (numeric) = 1.8553240561782586331884433124716 absolute error = 6e-31 relative error = 3.2339364005009823024837342441978e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 26.99 y[1] (analytic) = 1.865965989746639652006574146954 y[1] (numeric) = 1.8659659897466396520065741469531 absolute error = 9e-31 relative error = 4.8232390351455534944663985980791e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27 y[1] (analytic) = 1.876611372780421951793136752648 y[1] (numeric) = 1.8766113727804219517931367526487 absolute error = 7e-31 relative error = 3.7301276660327764903031413567982e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.01 y[1] (analytic) = 1.88726020409013465736697794218 y[1] (numeric) = 1.8872602040901346573669779421808 absolute error = 8e-31 relative error = 4.2389491298879334460768939319546e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.02 y[1] (analytic) = 1.897912482487126935564093400241 y[1] (numeric) = 1.8979124824871269355640934002392 absolute error = 1.8e-30 relative error = 9.4841043336265056079600525155503e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.03 y[1] (analytic) = 1.908568206783567147502877065176 y[1] (numeric) = 1.9085682067835671475028770651763 absolute error = 3e-31 relative error = 1.5718589408212865165290146703528e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.04 y[1] (analytic) = 1.919227375792442002017451577779 y[1] (numeric) = 1.9192273757924420020174515777791 absolute error = 1e-31 relative error = 5.2104300543707263326955007347000e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.05 y[1] (analytic) = 1.929889988327555710257068638116 y[1] (numeric) = 1.9298899883275557102570686381168 absolute error = 8e-31 relative error = 4.1453140066977635029305821208916e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.06 y[1] (analytic) = 1.940556043203529141449572265222 y[1] (numeric) = 1.9405560432035291414495722652204 absolute error = 1.6e-30 relative error = 8.2450594797492741738281110105648e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 9.14 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.07 y[1] (analytic) = 1.951225539235798979826922098203 y[1] (numeric) = 1.9512255392357989798269220982036 absolute error = 6e-31 relative error = 3.0749905017899216707107999778297e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 56.57 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.08 y[1] (analytic) = 1.961898475240616882710778011305 y[1] (numeric) = 1.9618984752406168827107780113055 absolute error = 5e-31 relative error = 2.5485518558175011563870167598418e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.09 y[1] (analytic) = 1.972574850035048639756151439261 y[1] (numeric) = 1.9725748500350486397561514392609 absolute error = 1e-31 relative error = 5.0695161199192620527301902712253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 97.98 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.1 y[1] (analytic) = 1.983254662436973333351132923402 y[1] (numeric) = 1.9832546624369733333511329234004 absolute error = 1.6e-30 relative error = 8.0675468980567545187948976709689e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 86.15 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.11 y[1] (analytic) = 1.993937911265082500170709492986 y[1] (numeric) = 1.9939379112650825001707094929874 absolute error = 1.4e-30 relative error = 7.0212818167028577358872762087653e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.12 y[1] (analytic) = 2.004624595338879293882689590532 y[1] (numeric) = 2.0046245953388792938826895905315 absolute error = 5e-31 relative error = 2.4942325917909613498055920384674e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.13 y[1] (analytic) = 2.01531471347867764900375733421 y[1] (numeric) = 2.0153147134786776490037573342103 absolute error = 3e-31 relative error = 1.4886012491923090791887495978867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 69.82 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.14 y[1] (analytic) = 2.026008264505601445903681985109 y[1] (numeric) = 2.0260082645056014459036819851091 absolute error = 1e-31 relative error = 4.9358140216867571937621217976547e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.15 y[1] (analytic) = 2.036705247241583676955712551777 y[1] (numeric) = 2.0367052472415836769557125517758 absolute error = 1.2e-30 relative error = 5.8918687504007891835797474908499e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.05 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.16 y[1] (analytic) = 2.047405660509365613831191519617 y[1] (numeric) = 2.0474056605093656138311915196173 absolute error = 3e-31 relative error = 1.4652689781338410325216417140521e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.17 y[1] (analytic) = 2.058109503132495975936425737958 y[1] (numeric) = 2.0581095031324959759364257379575 absolute error = 5e-31 relative error = 2.4294139803493791183957292061099e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.18 y[1] (analytic) = 2.068816773935330099989856533163 y[1] (numeric) = 2.0688167739353300999898565331621 absolute error = 9e-31 relative error = 4.3503127552857584723436613652449e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=104044496, alloc=4521156, time=4.15 TOP MAIN SOLVE Loop x[1] = 27.19 y[1] (analytic) = 2.079527471743029110737575142144 y[1] (numeric) = 2.0795274717430291107375751421419 absolute error = 2.1e-30 relative error = 1.0098447981741790212828949525711e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.2 y[1] (analytic) = 2.090241595381559092805233576797 y[1] (numeric) = 2.0902415953815590928052335767957 absolute error = 1.3e-30 relative error = 6.2193767594730791135373509498628e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.09 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.21 y[1] (analytic) = 2.100959143677690263684405036578 y[1] (numeric) = 2.1009591436776902636844050365775 absolute error = 5e-31 relative error = 2.3798654129216392766300162198100e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 31.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.22 y[1] (analytic) = 2.111680115458996147851451983395 y[1] (numeric) = 2.1116801154589961478514519833933 absolute error = 1.7e-30 relative error = 8.0504617510710750183073641427238e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 22.49 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.23 y[1] (analytic) = 2.12240450955385275201696398048 y[1] (numeric) = 2.1224045095538527520169639804786 absolute error = 1.4e-30 relative error = 6.5962920531783630380703897736014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.24 y[1] (analytic) = 2.133132324791437741503831374804 y[1] (numeric) = 2.1331323247914377415038313748042 absolute error = 2e-31 relative error = 9.3758834215572891952667649430496e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.25 y[1] (analytic) = 2.143863560001729617752024870934 y[1] (numeric) = 2.143863560001729617752024870932 absolute error = 2.0e-30 relative error = 9.3289518853447299039922679905860e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.26 y[1] (analytic) = 2.154598214015506896948155003117 y[1] (numeric) = 2.1545982140155068969481550031181 absolute error = 1.1e-30 relative error = 5.1053602144686599583670795545843e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.27 y[1] (analytic) = 2.165336285664347289777889461867 y[1] (numeric) = 2.1653362856643472897778894618669 absolute error = 1e-31 relative error = 4.6182203042572197312388805259467e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 10.77 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.28 y[1] (analytic) = 2.176077773780626882299310171102 y[1] (numeric) = 2.1760777737806268822993101711002 absolute error = 1.8e-30 relative error = 8.2717631772542530812485699903552e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.29 y[1] (analytic) = 2.186822677197519317935295942647 y[1] (numeric) = 2.1868226771975193179352959426463 absolute error = 7e-31 relative error = 3.2009911333875117002074003886595e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.3 y[1] (analytic) = 2.197570994748994980583020455903 y[1] (numeric) = 2.197570994748994980583020455902 absolute error = 1.0e-30 relative error = 4.5504786984787233206398429695818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.31 y[1] (analytic) = 2.208322725269820178838659222299 y[1] (numeric) = 2.2083227252698201788386592222997 absolute error = 7e-31 relative error = 3.1698265474964565399140093415853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.32 y[1] (analytic) = 2.219077867595556331335403096651 y[1] (numeric) = 2.2190778675955563313354030966495 absolute error = 1.5e-30 relative error = 6.7595645105743820023677120849850e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.33 y[1] (analytic) = 2.229836420562559153192879790547 y[1] (numeric) = 2.2298364205625591531928797905463 absolute error = 7e-31 relative error = 3.1392437290238490705673760935036e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.34 y[1] (analytic) = 2.240598383007977843576088726862 y[1] (numeric) = 2.2405983830079778435760887268614 absolute error = 6e-31 relative error = 2.6778560787610085868228381827943e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.35 y[1] (analytic) = 2.251363753769754274361958448901 y[1] (numeric) = 2.2513637537697542743619584488999 absolute error = 1.1e-30 relative error = 4.8859274657776887682685955590348e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.36 y[1] (analytic) = 2.26213253168662217991163966313 y[1] (numeric) = 2.2621325316866221799116396631285 absolute error = 1.5e-30 relative error = 6.6309112264152613783874668998440e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.37 y[1] (analytic) = 2.272904715598106347946650850484 y[1] (numeric) = 2.2729047155981063479466508504842 absolute error = 2e-31 relative error = 8.7993129948419659291417171377466e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.38 y[1] (analytic) = 2.283680304344521811526997228188 y[1] (numeric) = 2.2836803043445218115269972281888 absolute error = 8e-31 relative error = 3.5031173079614648544385476728370e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.16 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.39 y[1] (analytic) = 2.294459296766973042129387681746 y[1] (numeric) = 2.2944592967669730421293876817466 absolute error = 6e-31 relative error = 2.6149951792364980756787849634841e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.4 y[1] (analytic) = 2.30524169170735314382367811541 y[1] (numeric) = 2.3052416917073531438236781154106 absolute error = 6e-31 relative error = 2.6027639624876655627444037710582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 8.356 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.41 y[1] (analytic) = 2.316027488008343048545673488896 y[1] (numeric) = 2.3160274880083430485456734888964 absolute error = 4e-31 relative error = 1.7270952183040716832591792528516e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.42 y[1] (analytic) = 2.326816684513410712464424618527 y[1] (numeric) = 2.3268166845134107124644246185264 absolute error = 6e-31 relative error = 2.5786302977515110432520198156928e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 23.05 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.43 y[1] (analytic) = 2.337609280066810313442159622324 y[1] (numeric) = 2.3376092800668103134421596223238 absolute error = 2e-31 relative error = 8.5557497442123380336069236865424e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.44 y[1] (analytic) = 2.348405273513581449584993680869 y[1] (numeric) = 2.3484052735135814495849936808699 absolute error = 9e-31 relative error = 3.8323879193707451094611619205825e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.45 y[1] (analytic) = 2.359204663699548338882564569017 y[1] (numeric) = 2.3592046636995483388825645690171 absolute error = 1e-31 relative error = 4.2387166123682813502576725948642e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.46 y[1] (analytic) = 2.370007449471319019934745187836 y[1] (numeric) = 2.3700074494713190199347451878355 absolute error = 5e-31 relative error = 2.1096980100696971275788037261577e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=108047712, alloc=4521156, time=4.31 x[1] = 27.47 y[1] (analytic) = 2.380813629676284553763588091489 y[1] (numeric) = 2.3808136296762845537635880914881 absolute error = 9e-31 relative error = 3.7802202943637027562975966406698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.48 y[1] (analytic) = 2.391623203162618226708660760103 y[1] (numeric) = 2.3916232031626182267086607601032 absolute error = 2e-31 relative error = 8.3625213091897325993145490819764e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.81 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.49 y[1] (analytic) = 2.402436168779274754403934117167 y[1] (numeric) = 2.4024361687792747544039341171683 absolute error = 1.3e-30 relative error = 5.4111739445737518356014535880548e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 102.8 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.5 y[1] (analytic) = 2.413252525375989486834390528527 y[1] (numeric) = 2.4132525253759894868343905285258 absolute error = 1.2e-30 relative error = 4.9725421910126775536425834425431e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.51 y[1] (analytic) = 2.424072271803277614470521249742 y[1] (numeric) = 2.424072271803277614470521249742 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.52 y[1] (analytic) = 2.434895406912433375478887009459 y[1] (numeric) = 2.4348954069124333754788870094587 absolute error = 3e-31 relative error = 1.2320857772712902376574727023717e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.53 y[1] (analytic) = 2.445721929555529264006919128357 y[1] (numeric) = 2.4457219295555292640069191283568 absolute error = 2e-31 relative error = 8.1775445353408100806615927866758e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.54 y[1] (analytic) = 2.456551838585415239540142276576 y[1] (numeric) = 2.4565518385854152395401422765768 absolute error = 8e-31 relative error = 3.2565972654608147258460111686342e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.55 y[1] (analytic) = 2.467385132855717937330003666889 y[1] (numeric) = 2.4673851328557179373300036668869 absolute error = 2.1e-30 relative error = 8.5110345038412734951296019538503e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.56 y[1] (analytic) = 2.478221811220839879890497166579 y[1] (numeric) = 2.4782218112208398798904971665783 absolute error = 7e-31 relative error = 2.8246059203843454381591406109767e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.57 y[1] (analytic) = 2.489061872535958689561774488033 y[1] (numeric) = 2.4890618725359586895617744880325 absolute error = 5e-31 relative error = 2.0087889558590177559120296498076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 25.37 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.58 y[1] (analytic) = 2.499905315657026302138939286162 y[1] (numeric) = 2.4999053156570263021389392861627 absolute error = 7e-31 relative error = 2.8001060504806585748851943371251e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 83.91 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.59 y[1] (analytic) = 2.510752139440768181564223650512 y[1] (numeric) = 2.5107521394407681815642236505108 absolute error = 1.2e-30 relative error = 4.7794442993774834845519140518167e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 33.07 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.6 y[1] (analytic) = 2.521602342744682535680750130701 y[1] (numeric) = 2.5216023427446825356807501307021 absolute error = 1.1e-30 relative error = 4.3623055917797316237181517461757e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.61 y[1] (analytic) = 2.532455924427039533046086076246 y[1] (numeric) = 2.5324559244270395330460860762461 absolute error = 1e-31 relative error = 3.9487360484911379653018977233946e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.62 y[1] (analytic) = 2.54331288334688052080380070535 y[1] (numeric) = 2.5433128833468805208038007053484 absolute error = 1.6e-30 relative error = 6.2910073332954418490420345525021e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 39.33 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.63 y[1] (analytic) = 2.554173218364017243611238942489 y[1] (numeric) = 2.5541732183640172436112389424887 absolute error = 3e-31 relative error = 1.1745483737870922027990505385741e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.64 y[1] (analytic) = 2.565036928339031063621729681044 y[1] (numeric) = 2.5650369283390310636217296810423 absolute error = 1.7e-30 relative error = 6.6275848944631813285094500508131e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.64 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.65 y[1] (analytic) = 2.575904012133272181519449735208 y[1] (numeric) = 2.5759040121332721815194497352087 absolute error = 7e-31 relative error = 2.7174925645629352114452211659186e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.66 y[1] (analytic) = 2.586774468608858858605168344977 y[1] (numeric) = 2.5867744686088588586051683449755 absolute error = 1.5e-30 relative error = 5.7987274043518947594714681018522e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 24.49 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.67 y[1] (analytic) = 2.597648296628676639931100688817 y[1] (numeric) = 2.5976482966286766399311006888154 absolute error = 1.6e-30 relative error = 6.1594173548302853826490405029148e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.68 y[1] (analytic) = 2.608525495056377578483102441317 y[1] (numeric) = 2.6085254950563775784831024413158 absolute error = 1.2e-30 relative error = 4.6003000632894508942248532074507e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.69 y[1] (analytic) = 2.619406062756379460408440986987 y[1] (numeric) = 2.6194060627563794604084409869855 absolute error = 1.5e-30 relative error = 5.7264889981264009694279614920719e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.7 y[1] (analytic) = 2.630289998593865031287382467111 y[1] (numeric) = 2.6302899985938650312873824671097 absolute error = 1.3e-30 relative error = 4.9424208003489009643283409675568e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.89 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.71 y[1] (analytic) = 2.641177301434781223446837393743 y[1] (numeric) = 2.6411773014347812234468373937412 absolute error = 1.8e-30 relative error = 6.8151426222774825947671237027493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.72 y[1] (analytic) = 2.652067970145838384314311113755 y[1] (numeric) = 2.6520679701458383843143111137534 absolute error = 1.6e-30 relative error = 6.0330278786633635794985070702030e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.73 y[1] (analytic) = 2.66296200359450950581040894636 y[1] (numeric) = 2.6629620035945095058104089463609 absolute error = 9e-31 relative error = 3.3796952370524451132508922774156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.74 y[1] (analytic) = 2.673859400649029454778149349657 y[1] (numeric) = 2.6738594006490294547781493496561 absolute error = 9e-31 relative error = 3.3659211841188874811611618795647e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.75 y[1] (analytic) = 2.684760160178394204447341995539 y[1] (numeric) = 2.6847601601783942044473419955383 absolute error = 7e-31 relative error = 2.6073092501249240604701793357712e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=112048628, alloc=4521156, time=4.47 TOP MAIN SOLVE Loop x[1] = 27.76 y[1] (analytic) = 2.695664281052360066932291147952 y[1] (numeric) = 2.6956642810523600669322911479511 absolute error = 9e-31 relative error = 3.3386946821458386653513547698256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.77 y[1] (analytic) = 2.706571762141442926761088246612 y[1] (numeric) = 2.7065717621414429267610882466123 absolute error = 3e-31 relative error = 1.1084132488053434387483297490834e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 107.7 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.78 y[1] (analytic) = 2.717482602316917475434761097443 y[1] (numeric) = 2.7174826023169174754347610974416 absolute error = 1.4e-30 relative error = 5.1518269107090666192906202922109e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.79 y[1] (analytic) = 2.728396800450816447014550561691 y[1] (numeric) = 2.72839680045081644701455056169 absolute error = 1.0e-30 relative error = 3.6651560353492891423966986714871e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.8 y[1] (analytic) = 2.739314355415929854735589118369 y[1] (numeric) = 2.7393143554159298547355891183679 absolute error = 1.1e-30 relative error = 4.0156033856617345646429012689793e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.81 y[1] (analytic) = 2.750235266085804228645259148985 y[1] (numeric) = 2.7502352660858042286452591489841 absolute error = 9e-31 relative error = 3.2724473105928131832530762390898e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 40.95 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.82 y[1] (analytic) = 2.761159531334741854264512259863 y[1] (numeric) = 2.7611595313347418542645122598632 absolute error = 2e-31 relative error = 7.2433337418689528925266863570851e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.83 y[1] (analytic) = 2.772087150037800012270434415426 y[1] (numeric) = 2.7720871500378000122704344154262 absolute error = 2e-31 relative error = 7.2147803865860715139704597459952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.84 y[1] (analytic) = 2.783018121070790219198345105825 y[1] (numeric) = 2.783018121070790219198345105825 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.75 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.85 y[1] (analytic) = 2.793952443310277469161722214231 y[1] (numeric) = 2.7939524433102774691617222142298 absolute error = 1.2e-30 relative error = 4.2949907858067865935064356114244e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.75 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.86 y[1] (analytic) = 2.804890115633579476588247682909 y[1] (numeric) = 2.8048901156335794765882476829091 absolute error = 1e-31 relative error = 3.5652020534648150196908575394706e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.87 y[1] (analytic) = 2.815831136918765919970272503032 y[1] (numeric) = 2.8158311369187659199702725030304 absolute error = 1.6e-30 relative error = 5.6821589157892691319106097070422e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 31.15 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.88 y[1] (analytic) = 2.826775506044657686628002970871 y[1] (numeric) = 2.8267755060446576866280029708702 absolute error = 8e-31 relative error = 2.8300797084498351342541232742359e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.89 y[1] (analytic) = 2.837723221890826118483713562879 y[1] (numeric) = 2.8377232218908261184837135628777 absolute error = 1.3e-30 relative error = 4.5811374061131535372778597243256e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 12.03 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.9 y[1] (analytic) = 2.848674283337592258845295183803 y[1] (numeric) = 2.8486742833375922588452951838026 absolute error = 4e-31 relative error = 1.4041619371497537403271559733833e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.91 y[1] (analytic) = 2.859628689266026100197450935905 y[1] (numeric) = 2.8596286892660261001974509359053 absolute error = 3e-31 relative error = 1.0490872508241630002392184252425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.92 y[1] (analytic) = 2.870586438557945832998854943128 y[1] (numeric) = 2.8705864385579458329988549431263 absolute error = 1.7e-30 relative error = 5.9221348542773856495167666614364e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.93 y[1] (analytic) = 2.881547530095917095483593142037 y[1] (numeric) = 2.8815475300959170954835931420358 absolute error = 1.2e-30 relative error = 4.1644289655706494868313759848722e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 20.82 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 27.94 y[1] (analytic) = 2.892511962763252224465208321421 y[1] (numeric) = 2.892511962763252224465208321421 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.95 y[1] (analytic) = 2.903479735444009507141675054535 y[1] (numeric) = 2.9034797354440095071416750545335 absolute error = 1.5e-30 relative error = 5.1662148066296565730707061707606e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.96 y[1] (analytic) = 2.914450847022992433899633522318 y[1] (numeric) = 2.914450847022992433899633522318 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.97 y[1] (analytic) = 2.925425296385748952116214572415 y[1] (numeric) = 2.9254252963857489521162145724133 absolute error = 1.7e-30 relative error = 5.8111208722379100576812553046168e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.98 y[1] (analytic) = 2.936403082418570720956791697364 y[1] (numeric) = 2.9364030824185707209567916973628 absolute error = 1.2e-30 relative error = 4.0866324081488807423325450528839e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 27.99 y[1] (analytic) = 2.947384204008492367166998946328 y[1] (numeric) = 2.9473842040084923671669989463278 absolute error = 2e-31 relative error = 6.7856779488740089384631694293189e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28 y[1] (analytic) = 2.958368660043290741857357107675 y[1] (numeric) = 2.9583686600432907418573571076754 absolute error = 4e-31 relative error = 1.3520965300996214373597471161061e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 63.33 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.01 y[1] (analytic) = 2.96935644941148417827885381514 y[1] (numeric) = 2.9693564494114841782788538151396 absolute error = 4e-31 relative error = 1.3470932399486042455574351728698e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.02 y[1] (analytic) = 2.980347571002331750587826537844 y[1] (numeric) = 2.9803475710023317505878265378455 absolute error = 1.5e-30 relative error = 5.0329700287122197430364865771435e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 52.39 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.03 y[1] (analytic) = 2.991342023705832533598500714368 y[1] (numeric) = 2.9913420237058325335985007143667 absolute error = 1.3e-30 relative error = 4.3458754956729799827993458474433e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=116052160, alloc=4521156, time=4.63 x[1] = 28.04 y[1] (analytic) = 3.002339806412724863521538583175 y[1] (numeric) = 3.0023398064127248635215385831746 absolute error = 4e-31 relative error = 1.3322942298058213354124443260152e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.05 y[1] (analytic) = 3.013340918014485599686957546354 y[1] (numeric) = 3.0133409180144855996869575463544 absolute error = 4e-31 relative error = 1.3274302871231815185700108280678e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.06 y[1] (analytic) = 3.024345357403329387249780180327 y[1] (numeric) = 3.0243453574033293872497801803267 absolute error = 3e-31 relative error = 9.9195020590365643591099472682987e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.07 y[1] (analytic) = 3.03535312347220792087678127655 y[1] (numeric) = 3.0353531234722079208767812765499 absolute error = 1e-31 relative error = 3.2945095984617360357784586158052e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.08 y[1] (analytic) = 3.0463642151148092094127005568 y[1] (numeric) = 3.0463642151148092094127005568013 absolute error = 1.3e-30 relative error = 4.2673820600633812393381799745766e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.09 y[1] (analytic) = 3.057378631225556841524292961671 y[1] (numeric) = 3.057378631225556841524292961669 absolute error = 2.0e-30 relative error = 6.5415515748479463641901253000729e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.1 y[1] (analytic) = 3.068396370699609252320591657351 y[1] (numeric) = 3.0683963706996092523205916573507 absolute error = 3e-31 relative error = 9.7770940829133670624127672568411e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.11 y[1] (analytic) = 3.07941743243285899094776214477 y[1] (numeric) = 3.0794174324328589909477621447689 absolute error = 1.1e-30 relative error = 3.5721042182025884474335153383884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.12 y[1] (analytic) = 3.090441815321931989156929086395 y[1] (numeric) = 3.0904418153219319891569290863962 absolute error = 1.2e-30 relative error = 3.8829399539269298350648251560878e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 32.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.13 y[1] (analytic) = 3.101469518264186830843360690058 y[1] (numeric) = 3.1014695182641868308433606900591 absolute error = 1.1e-30 relative error = 3.5467058229082382452459682329411e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.14 y[1] (analytic) = 3.112500540157714022555398705372 y[1] (numeric) = 3.1125005401577140225553987053711 absolute error = 9e-31 relative error = 2.8915657632444810859358891026024e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.15 y[1] (analytic) = 3.123534879901335264971525297364 y[1] (numeric) = 3.1235348799013352649715252973631 absolute error = 9e-31 relative error = 2.8813508880311551769486416642814e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.16 y[1] (analytic) = 3.134572536394602725343961263341 y[1] (numeric) = 3.1345725363946027253439612633396 absolute error = 1.4e-30 relative error = 4.4663187204794607632726514919935e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.17 y[1] (analytic) = 3.145613508537798310907193253025 y[1] (numeric) = 3.1456135085377983109071932530255 absolute error = 5e-31 relative error = 1.5895150457705757961232071247874e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.18 y[1] (analytic) = 3.156657795231932943249830838689 y[1] (numeric) = 3.1566577952319329432498308386898 absolute error = 8e-31 relative error = 2.5343260242158134553349595254509e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.19 y[1] (analytic) = 3.167705395378745833648197461165 y[1] (numeric) = 3.1677053953787458336481974611637 absolute error = 1.3e-30 relative error = 4.1039169927118991244993375596318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.55 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.2 y[1] (analytic) = 3.178756307880703759360062449532 y[1] (numeric) = 3.1787563078807037593600624495323 absolute error = 3e-31 relative error = 9.4376533129087782090822262071203e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.21 y[1] (analytic) = 3.189810531641000340876924476784 y[1] (numeric) = 3.1898105316410003408769244767852 absolute error = 1.2e-30 relative error = 3.7619789266375615416304851973447e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 24.49 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.22 y[1] (analytic) = 3.200868065563555320133259970891 y[1] (numeric) = 3.2008680655635553201332599708891 absolute error = 1.9e-30 relative error = 5.9358897682822168246287817393540e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.23 y[1] (analytic) = 3.211928908553013839671153150604 y[1] (numeric) = 3.2119289085530138396711531506055 absolute error = 1.5e-30 relative error = 4.6700909101869122360239317067790e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 29.03 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.24 y[1] (analytic) = 3.22299305951474572275872749795 y[1] (numeric) = 3.2229930595147457227587274979486 absolute error = 1.4e-30 relative error = 4.3437884418242718527065119726542e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.25 y[1] (analytic) = 3.234060517354844754460801614467 y[1] (numeric) = 3.2340605173548447544608016144684 absolute error = 1.4e-30 relative error = 4.3289233225142843752613616424346e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.26 y[1] (analytic) = 3.24513128098012796366019553659 y[1] (numeric) = 3.2451312809801279636601955365881 absolute error = 1.9e-30 relative error = 5.8549249182490467265451353349014e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.27 y[1] (analytic) = 3.256205349298134906028116706024 y[1] (numeric) = 3.2562053492981349060281167060229 absolute error = 1.1e-30 relative error = 3.3781653243616887745840950419318e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.28 y[1] (analytic) = 3.267282721217126947942057904898 y[1] (numeric) = 3.2672827212171269479420579048976 absolute error = 4e-31 relative error = 1.2242589152217355353396887585853e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.62 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.29 y[1] (analytic) = 3.278363395646086551349642571566 y[1] (numeric) = 3.2783633956460865513496425715657 absolute error = 3e-31 relative error = 9.1509074435867173803815863700367e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.3 y[1] (analytic) = 3.289447371494716559576856012344 y[1] (numeric) = 3.2894473714947165595768560123434 absolute error = 6e-31 relative error = 1.8240145904123753123920101506176e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.31 y[1] (analytic) = 3.30053464767343948407910411642 y[1] (numeric) = 3.3005346476734394840791041164211 absolute error = 1.1e-30 relative error = 3.3327933726597736123003785198626e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 53.85 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.32 y[1] (analytic) = 3.311625223093396792133544266125 y[1] (numeric) = 3.3116252230933967921335442661237 absolute error = 1.3e-30 relative error = 3.9255649791967310497898215485328e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 15.16 Order of pole (six term test) = -0.5 bytes used=120053212, alloc=4521156, time=4.80 TOP MAIN SOLVE Loop x[1] = 28.33 y[1] (analytic) = 3.322719096666448195471136212477 y[1] (numeric) = 3.3227190966664481954711362124768 absolute error = 2e-31 relative error = 6.0191666578330993655104635228426e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 71.55 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.34 y[1] (analytic) = 3.333816267305170939846863756718 y[1] (numeric) = 3.3338162673051709398468637567191 absolute error = 1.1e-30 relative error = 3.2995219646257373610115009315348e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 72.57 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.35 y[1] (analytic) = 3.344916733922859095546581142001 y[1] (numeric) = 3.3449167339228590955465811420003 absolute error = 7e-31 relative error = 2.0927277289173425833276461359902e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.36 y[1] (analytic) = 3.356020495433522848828941116035 y[1] (numeric) = 3.3560204954335228488289411160351 absolute error = 1e-31 relative error = 2.9797195856243492567016460289255e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 24.32 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.37 y[1] (analytic) = 3.367127550751887794300864674969 y[1] (numeric) = 3.3671275507518877943008646749693 absolute error = 3e-31 relative error = 8.9096713883918436151420916948242e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.38 y[1] (analytic) = 3.378237898793394228225015541171 y[1] (numeric) = 3.3782378987933942282250155411706 absolute error = 4e-31 relative error = 1.1840492350845630620385820724313e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.39 y[1] (analytic) = 3.389351538474196442757745463105 y[1] (numeric) = 3.3893515384741964427577454631029 absolute error = 2.1e-30 relative error = 6.1958754533481318396818012152559e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.4 y[1] (analytic) = 3.400468468711162021115979453895 y[1] (numeric) = 3.4004684687111620211159794538954 absolute error = 4e-31 relative error = 1.1763085106670820222109673955172e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.41 y[1] (analytic) = 3.411588688421871133671513106702 y[1] (numeric) = 3.4115886884218711336715131067011 absolute error = 9e-31 relative error = 2.6380671358607446604046384567567e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 14.56 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.42 y[1] (analytic) = 3.422712196524615834971197139464 y[1] (numeric) = 3.4227121965246158349711971394628 absolute error = 1.2e-30 relative error = 3.5059915385771165556647970852597e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.43 y[1] (analytic) = 3.433838991938399361681487329294 y[1] (numeric) = 3.4338389919383993616814873292946 absolute error = 6e-31 relative error = 1.7473154722997087303263622276004e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.44 y[1] (analytic) = 3.444969073582935431455840997357 y[1] (numeric) = 3.4449690735829354314558409973574 absolute error = 4e-31 relative error = 1.1611134714309076230021164417003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 384.2 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.45 y[1] (analytic) = 3.456102440378647542723444198876 y[1] (numeric) = 3.4561024403786475427234441988764 absolute error = 4e-31 relative error = 1.1573731013487446046767312008690e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.46 y[1] (analytic) = 3.467239091246668275397756759838 y[1] (numeric) = 3.4672390912466682753977567598363 absolute error = 1.7e-30 relative error = 4.9030365523156177490813088499118e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.47 y[1] (analytic) = 3.478379025108838592503365281913 y[1] (numeric) = 3.4783790251088385925033652819144 absolute error = 1.4e-30 relative error = 4.0248632765263237941599512231010e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 36.23 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.48 y[1] (analytic) = 3.48952224088770714271963721039 y[1] (numeric) = 3.4895222408877071427196372103883 absolute error = 1.7e-30 relative error = 4.8717270808038561384809313376145e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.49 y[1] (analytic) = 3.500668737506529563839672026106 y[1] (numeric) = 3.5006687375065295638396720261045 absolute error = 1.5e-30 relative error = 4.2848955798897614204105427203484e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 41.37 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.5 y[1] (analytic) = 3.511818513889267787143048582135 y[1] (numeric) = 3.5118185138892677871430485821335 absolute error = 1.5e-30 relative error = 4.2712913382838238381828000311855e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.51 y[1] (analytic) = 3.522971568960589342680870558484 y[1] (numeric) = 3.5229715689605893426808705584835 absolute error = 5e-31 relative error = 1.4192564152526471405734748215809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.52 y[1] (analytic) = 3.534127901645866665471614954216 y[1] (numeric) = 3.5341279016458666654716149542171 absolute error = 1.1e-30 relative error = 3.1125076132296251851436224992925e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.53 y[1] (analytic) = 3.545287510871176402606291475531 y[1] (numeric) = 3.5452875108711764026062914755304 absolute error = 6e-31 relative error = 1.6923874246028729025754931895604e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.84 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.54 y[1] (analytic) = 3.556450395563298721261423610831 y[1] (numeric) = 3.5564503955632987212614236108299 absolute error = 1.1e-30 relative error = 3.0929715802370225562936779042263e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.316 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.55 y[1] (analytic) = 3.567616554649716617618365109599 y[1] (numeric) = 3.5676165546497166176183651095981 absolute error = 9e-31 relative error = 2.5226926330606337564261334497025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.56 y[1] (analytic) = 3.57878598705861522668746850089 y[1] (numeric) = 3.578785987058615226687468500889 absolute error = 1.0e-30 relative error = 2.7942436446776594510419940360067e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.57 y[1] (analytic) = 3.589958691718881133035625199659 y[1] (numeric) = 3.5899586917188811330356251996589 absolute error = 1e-31 relative error = 2.7855473721932926132807352211035e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.58 y[1] (analytic) = 3.601134667560101682415699654837 y[1] (numeric) = 3.6011346675601016824156996548349 absolute error = 2.1e-30 relative error = 5.8314953309503017411415896766627e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.59 y[1] (analytic) = 3.612313913512564294296382892065 y[1] (numeric) = 3.6123139135125642942963828920658 absolute error = 8e-31 relative error = 2.2146469524906018453443914897171e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.6 y[1] (analytic) = 3.623496428507255775290993696513 y[1] (numeric) = 3.6234964285072557752909936965131 absolute error = 1e-31 relative error = 2.7597653805663122547611328868459e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=124054068, alloc=4521156, time=4.95 x[1] = 28.61 y[1] (analytic) = 3.634682211475861633483758566832 y[1] (numeric) = 3.6346822114758616334837585668313 absolute error = 7e-31 relative error = 1.9258905160673323561473034791052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.62 y[1] (analytic) = 3.645871261350765393652104450683 y[1] (numeric) = 3.6458712613507653936521044506826 absolute error = 4e-31 relative error = 1.0971314435600868731035383949373e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.63 y[1] (analytic) = 3.657063577065047913383501144742 y[1] (numeric) = 3.6570635770650479133835011447423 absolute error = 3e-31 relative error = 8.2033028323987467467261635504839e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.64 y[1] (analytic) = 3.6682591575524867000853931082 y[1] (numeric) = 3.6682591575524867000853931082002 absolute error = 2e-31 relative error = 5.4521774882841911627832134053668e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.65 y[1] (analytic) = 3.67945800174755522888676329826 y[1] (numeric) = 3.679458001747555228886763298261 absolute error = 1.0e-30 relative error = 2.7177915864919531903887842152252e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.66 y[1] (analytic) = 3.690660108585422261429874489117 y[1] (numeric) = 3.6906601085854222614298744891178 absolute error = 8e-31 relative error = 2.1676339095518299228648686253954e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.67 y[1] (analytic) = 3.701865477001951165550736382326 y[1] (numeric) = 3.7018654770019511655507363823265 absolute error = 5e-31 relative error = 1.3506703663498263360883272122799e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.68 y[1] (analytic) = 3.71307410593369923584684965647 y[1] (numeric) = 3.7130741059336992358468496564688 absolute error = 1.2e-30 relative error = 3.2318234588486482432003857269210e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.69 y[1] (analytic) = 3.724285994317917015130780937469 y[1] (numeric) = 3.7242859943179170151307809374696 absolute error = 6e-31 relative error = 1.6110470595314385320534391587547e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.7 y[1] (analytic) = 3.735501141092547616768125497954 y[1] (numeric) = 3.7355011410925476167681254979522 absolute error = 1.8e-30 relative error = 4.8186305719439337803378707187596e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.71 y[1] (analytic) = 3.746719545196226047898417314582 y[1] (numeric) = 3.7467195451962260478984173145829 absolute error = 9e-31 relative error = 2.4021013292919540230763402728959e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.72 y[1] (analytic) = 3.757941205568278533537548926501 y[1] (numeric) = 3.7579412055682785335375489265005 absolute error = 5e-31 relative error = 1.3305157602229959462422932697809e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 19.06 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.73 y[1] (analytic) = 3.769166121148721841560266345651 y[1] (numeric) = 3.7691661211487218415602663456519 absolute error = 9e-31 relative error = 2.3877960564012197257096350190470e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.05 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 28.74 y[1] (analytic) = 3.780394290878262608561307071192 y[1] (numeric) = 3.7803942908782626085613070711904 absolute error = 1.6e-30 relative error = 4.2323627560771905740736698695694e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.67 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.75 y[1] (analytic) = 3.791625713698296666593752055045 y[1] (numeric) = 3.7916257136982966665937520550456 absolute error = 6e-31 relative error = 1.5824346739508966775692181731731e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.76 y[1] (analytic) = 3.802860388550908370783165254365 y[1] (numeric) = 3.802860388550908370783165254366 absolute error = 1.0e-30 relative error = 2.6295995588232811010143599526811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.77 y[1] (analytic) = 3.814098314378869927816097188779 y[1] (numeric) = 3.8140983143788699278160971887799 absolute error = 9e-31 relative error = 2.3596664947179422196394254122679e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.78 y[1] (analytic) = 3.825339490125640725301531696337 y[1] (numeric) = 3.8253394901256407253015316963378 absolute error = 8e-31 relative error = 2.0913176518451295242781920460896e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.79 y[1] (analytic) = 3.836583914735366662003857851601 y[1] (numeric) = 3.8365839147353666620038578516001 absolute error = 9e-31 relative error = 2.3458368694695386693144034663603e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.8 y[1] (analytic) = 3.847831587152879478945951772642 y[1] (numeric) = 3.8478315871528794789459517726426 absolute error = 6e-31 relative error = 1.5593198049604794204595053556725e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.81 y[1] (analytic) = 3.859082506323696091380955800778 y[1] (numeric) = 3.8590825063236960913809558007768 absolute error = 1.2e-30 relative error = 3.1095474067569602924859012703062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.82 y[1] (analytic) = 3.870336671194017921631345287545 y[1] (numeric) = 3.8703366711940179216313452875447 absolute error = 3e-31 relative error = 7.7512636622242096246408659850395e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.83 y[1] (analytic) = 3.881594080710730232793875968064 y[1] (numeric) = 3.8815940807107302327938759680625 absolute error = 1.5e-30 relative error = 3.8643917133275976085526056210582e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.84 y[1] (analytic) = 3.892854733821401463309007638069 y[1] (numeric) = 3.8928547338214014633090076380706 absolute error = 1.6e-30 relative error = 4.1100942865889269078610295090462e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.85 y[1] (analytic) = 3.904118629474282562393402584115 y[1] (numeric) = 3.9041186294742825623934025841142 absolute error = 8e-31 relative error = 2.0491180620393333429339761224193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.86 y[1] (analytic) = 3.91538576661830632633409994215 y[1] (numeric) = 3.9153857666183063263340999421491 absolute error = 9e-31 relative error = 2.2986240785600144081339166693819e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.87 y[1] (analytic) = 3.926656144203086735642969879551 y[1] (numeric) = 3.9266561442030867356429698795505 absolute error = 5e-31 relative error = 1.2733480641999906927180963395608e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.88 y[1] (analytic) = 3.937929761178918293070054209024 y[1] (numeric) = 3.9379297611789182930700542090232 absolute error = 8e-31 relative error = 2.0315242996119359021708805532034e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.89 y[1] (analytic) = 3.949206616496775362474402750277 y[1] (numeric) = 3.9492066164967753624744027502768 absolute error = 2e-31 relative error = 5.0643083389091983606806158796868e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 202 Order of pole (six term test) = -0.5 bytes used=128055136, alloc=4521156, time=5.11 TOP MAIN SOLVE Loop x[1] = 28.9 y[1] (analytic) = 3.960486709108311508551017456562 y[1] (numeric) = 3.9604867091083115085510174565635 absolute error = 1.5e-30 relative error = 3.7874132907713236193997247971062e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.91 y[1] (analytic) = 3.971770037965858837412519018287 y[1] (numeric) = 3.9717700379658588374125190182868 absolute error = 2e-31 relative error = 5.0355382635000176539852420711126e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.92 y[1] (analytic) = 3.983056602022427338024153344901 y[1] (numeric) = 3.983056602022427338024153344901 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.93 y[1] (analytic) = 3.99434640023170422449075800924 y[1] (numeric) = 3.9943464002317042244907580092406 absolute error = 6e-31 relative error = 1.5021231007035222913720846972301e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.94 y[1] (analytic) = 4.00563943154805327919431141527 y[1] (numeric) = 4.0056394315480532791943114152706 absolute error = 6e-31 relative error = 1.4978881905207302382675891681441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.95 y[1] (analytic) = 4.016935694926514196780690121041 y[1] (numeric) = 4.0169356949265141967806901210411 absolute error = 1e-31 relative error = 2.4894598170018601590371184364754e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.96 y[1] (analytic) = 4.028235189322801928994262413381 y[1] (numeric) = 4.0282351893228019289942624133818 absolute error = 8e-31 relative error = 1.9859813600766698893013920573033e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.97 y[1] (analytic) = 4.039537913693306030358948889602 y[1] (numeric) = 4.0395379136933060303589488896021 absolute error = 1e-31 relative error = 2.4755306705011483965252789321728e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.98 y[1] (analytic) = 4.05084386699509000470438345418 y[1] (numeric) = 4.0508438669950900047043834541788 absolute error = 1.2e-30 relative error = 2.9623457220289219069916702386420e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 28.99 y[1] (analytic) = 4.062153048185890652535810785142 y[1] (numeric) = 4.06215304818589065253581078514 absolute error = 2.0e-30 relative error = 4.9234974071033002236195397723811e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 37.03 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29 y[1] (analytic) = 4.073465456224117419246358965598 y[1] (numeric) = 4.0734654562241174192463589655977 absolute error = 3e-31 relative error = 7.3647365670331179180539117457848e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.01 y[1] (analytic) = 4.08478109006885174417032861067 y[1] (numeric) = 4.0847810900688517441703286106685 absolute error = 1.5e-30 relative error = 3.6721674109951299419248793464057e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.02 y[1] (analytic) = 4.096099948679846410476142448853 y[1] (numeric) = 4.0960999486798464104761424488535 absolute error = 5e-31 relative error = 1.2206733386990413380219423012884e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.03 y[1] (analytic) = 4.107422031017524895897601939855 y[1] (numeric) = 4.1074220310175248958976019398548 absolute error = 2e-31 relative error = 4.8692342420546040005420018596933e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 33.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 63.49 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.04 y[1] (analytic) = 4.118747336042980724302100127793 y[1] (numeric) = 4.1187473360429807243021001277918 absolute error = 1.2e-30 relative error = 2.9135071954981351520510239219076e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.05 y[1] (analytic) = 4.130075862717976818094442539865 y[1] (numeric) = 4.1300758627179768180944425398643 absolute error = 7e-31 relative error = 1.6948841214246714220429299282692e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.06 y[1] (analytic) = 4.141407610004944851454930545708 y[1] (numeric) = 4.1414076100049448514549305457089 absolute error = 9e-31 relative error = 2.1731741590123880553254670162337e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.02 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.5 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.07 y[1] (analytic) = 4.152742576866984604410364192021 y[1] (numeric) = 4.1527425768669846044103641920222 absolute error = 1.2e-30 relative error = 2.8896566011210207542600382627124e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 43.78 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.08 y[1] (analytic) = 4.164080762267863317736624120493 y[1] (numeric) = 4.1640807622678633177366241204935 absolute error = 5e-31 relative error = 1.2007452029525176644930794322156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.09 y[1] (analytic) = 4.175422165172015048691494764723 y[1] (numeric) = 4.1754221651720150486914947647211 absolute error = 1.9e-30 relative error = 4.5504380750963552383558007823441e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.05 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.1 y[1] (analytic) = 4.18676678454454002757639360359 y[1] (numeric) = 4.1867667845445400275763936035888 absolute error = 1.2e-30 relative error = 2.8661734979598170530394254474958e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.11 y[1] (analytic) = 4.198114619351204015125673824573 y[1] (numeric) = 4.1981146193512040151256738245717 absolute error = 1.3e-30 relative error = 3.0966281721029045949939042880162e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.12 y[1] (analytic) = 4.209465668558437660722170320636 y[1] (numeric) = 4.2094656685584376607221703206361 absolute error = 1e-31 relative error = 2.3755984220735011288283050102877e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.13 y[1] (analytic) = 4.220819931133335861437661508815 y[1] (numeric) = 4.2208199311333358614376615088142 absolute error = 8e-31 relative error = 1.8953663341548696115402981078842e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 1.714 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.14 y[1] (analytic) = 4.232177406043657121896922017181 y[1] (numeric) = 4.2321774060436571218969220171815 absolute error = 5e-31 relative error = 1.1814249546486101123386697798491e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.15 y[1] (analytic) = 4.243538092257822914964043839862 y[1] (numeric) = 4.2435380922578229149640438398626 absolute error = 6e-31 relative error = 1.4139144905867055533731814206671e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 24.08 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.16 y[1] (analytic) = 4.25490198874491704324970610685 y[1] (numeric) = 4.2549019887449170432497061068502 absolute error = 2e-31 relative error = 4.7004607986045451160207429810703e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.17 y[1] (analytic) = 4.26626909447468500143807615686 y[1] (numeric) = 4.2662690944746850014380761568604 absolute error = 4e-31 relative error = 9.3758736531187531794932071616555e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=132056680, alloc=4521156, time=5.27 x[1] = 29.18 y[1] (analytic) = 4.277639408417533339432027137177 y[1] (numeric) = 4.2776394084175333394320271371779 absolute error = 9e-31 relative error = 2.1039641588979687131894019035493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 63.46 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.19 y[1] (analytic) = 4.289012929544529026315359884481 y[1] (numeric) = 4.2890129295445290263153598844816 absolute error = 6e-31 relative error = 1.3989232717554826640955293407048e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.2 y[1] (analytic) = 4.300389656827398815130719365 y[1] (numeric) = 4.3003896568273988151307193650015 absolute error = 1.5e-30 relative error = 3.4880560128279656032817320110079e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.21 y[1] (analytic) = 4.311769589238528608471898471052 y[1] (numeric) = 4.3117695892385286084718984710526 absolute error = 6e-31 relative error = 1.3915400338123396630556373805772e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.22 y[1] (analytic) = 4.323152725750962824889224484039 y[1] (numeric) = 4.323152725750962824889224484039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.23 y[1] (analytic) = 4.334539065338403766106726021433 y[1] (numeric) = 4.334539065338403766106726021433 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.24 y[1] (analytic) = 4.345928606975210985049780787025 y[1] (numeric) = 4.3459286069752109850497807870258 absolute error = 8e-31 relative error = 1.8408033641325833455215562012835e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.25 y[1] (analytic) = 4.357321349636400654681946939931 y[1] (numeric) = 4.3573213496364006546819469399324 absolute error = 1.4e-30 relative error = 3.2129831326689362866377464799477e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.26 y[1] (analytic) = 4.368717292297644937649683388427 y[1] (numeric) = 4.3687172922976449376496833884284 absolute error = 1.4e-30 relative error = 3.2046019605532686067109945690025e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.27 y[1] (analytic) = 4.380116433935271356733666799715 y[1] (numeric) = 4.3801164339352713567336667997131 absolute error = 1.9e-30 relative error = 4.3377842316693033571760178436461e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.25 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 107.2 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.28 y[1] (analytic) = 4.39151877352626216610541559615 y[1] (numeric) = 4.3915187735262621661054155961486 absolute error = 1.4e-30 relative error = 3.1879631448685362616158515249713e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.29 y[1] (analytic) = 4.402924310048253723387933682429 y[1] (numeric) = 4.4029243100482537233879336824293 absolute error = 3e-31 relative error = 6.8136533556878736931349544892099e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.3 y[1] (analytic) = 4.41433304247953586251908911651 y[1] (numeric) = 4.4143330424795358625190891165092 absolute error = 8e-31 relative error = 1.8122783041096489068017508736961e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.28 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 11.13 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.31 y[1] (analytic) = 4.425744969799051267416445399966 y[1] (numeric) = 4.4257449697990512674164453999643 absolute error = 1.7e-30 relative error = 3.8411612318393204842047635621794e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 64.81 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.32 y[1] (analytic) = 4.437160090986394846442265520811 y[1] (numeric) = 4.4371600909863948464422655208126 absolute error = 1.6e-30 relative error = 3.6059100126908310280838210668845e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.3 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.33 y[1] (analytic) = 4.448578405021813107667411333667 y[1] (numeric) = 4.4485784050218131076674113336676 absolute error = 6e-31 relative error = 1.3487454763586615193552499674888e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.31 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 53.44 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.34 y[1] (analytic) = 4.459999910886203534932863308473 y[1] (numeric) = 4.4599999108862035349328633084742 absolute error = 1.2e-30 relative error = 2.6905830134009118898152166897287e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.32 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.35 y[1] (analytic) = 4.471424607561113964707588119989 y[1] (numeric) = 4.4714246075611139647075881199885 absolute error = 5e-31 relative error = 1.1182118539011197317218951422753e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.34 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.36 y[1] (analytic) = 4.482852494028741963741483985621 y[1] (numeric) = 4.4828524940287419637414839856215 absolute error = 5e-31 relative error = 1.1153612586316658598371790900534e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.37 y[1] (analytic) = 4.494283569271934207512136089291 y[1] (numeric) = 4.4942835692719342075121360892919 absolute error = 9e-31 relative error = 2.0025438673995338678217746479273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 3.219 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.38 y[1] (analytic) = 4.505717832274185859464116853533 y[1] (numeric) = 4.5057178322741858594641168535331 absolute error = 1e-31 relative error = 2.2194021845688164044195878466884e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.37 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.39 y[1] (analytic) = 4.517155282019639951039568241296 y[1] (numeric) = 4.5171552820196399510395682412952 absolute error = 8e-31 relative error = 1.7710261216486595719560264383818e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.4 y[1] (analytic) = 4.528595917493086762498805682677 y[1] (numeric) = 4.5285959174930867624988056826776 absolute error = 6e-31 relative error = 1.3249139709778841059404414365656e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.41 y[1] (analytic) = 4.540039737679963204529685630248 y[1] (numeric) = 4.5400397376799632045296856302475 absolute error = 5e-31 relative error = 1.1013119463476511857179425144499e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.42 y[1] (analytic) = 4.551486741566352200644481149648 y[1] (numeric) = 4.5514867415663522006444811496479 absolute error = 1e-31 relative error = 2.1970842864761575012029280444795e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.43 y[1] (analytic) = 4.562936928138982070363012349895 y[1] (numeric) = 4.5629369281389820703630123498949 absolute error = 1e-31 relative error = 2.1915709459693436579059712005787e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 16.89 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.44 y[1] (analytic) = 4.57439029638522591318078085012 y[1] (numeric) = 4.5743902963852259131807808501199 absolute error = 1e-31 relative error = 2.1860836859290731399799133972349e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.45 y[1] (analytic) = 4.585846845293100993320859866544 y[1] (numeric) = 4.5858468452931009933208598665425 absolute error = 1.5e-30 relative error = 3.2709334842693129989765724937408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.46 y[1] (analytic) = 4.597306573851268125268293885176 y[1] (numeric) = 4.5973065738512681252682938851746 absolute error = 1.4e-30 relative error = 3.0452613448991464689896155580233e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 bytes used=136061196, alloc=4521156, time=5.43 TOP MAIN SOLVE Loop x[1] = 29.47 y[1] (analytic) = 4.608769481049031060085764262175 y[1] (numeric) = 4.6087694810490310600857642621752 absolute error = 2e-31 relative error = 4.3395531241557505683422471380222e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.48 y[1] (analytic) = 4.620235565876335872509279464906 y[1] (numeric) = 4.6202355658763358725092794649047 absolute error = 1.3e-30 relative error = 2.8137093476389110397771113131241e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.49 y[1] (analytic) = 4.631704827323770348822651032587 y[1] (numeric) = 4.6317048273237703488226510325873 absolute error = 3e-31 relative error = 6.4770966886795759417568290039345e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 56.62 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.5 y[1] (analytic) = 4.64317726438256337550951869609 y[1] (numeric) = 4.6431772643825633755095186960891 absolute error = 9e-31 relative error = 1.9383278922039593142516306989193e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.5 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.51 y[1] (analytic) = 4.654652876044584328681690451673 y[1] (numeric) = 4.6546528760445843286816904516717 absolute error = 1.3e-30 relative error = 2.7929042930150996370505095641087e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.52 y[1] (analytic) = 4.666131661302342464282565733704 y[1] (numeric) = 4.6661316613023424642825657337057 absolute error = 1.7e-30 relative error = 3.6432748224800858897394802032066e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.53 y[1] (analytic) = 4.677613619148986309064412176225 y[1] (numeric) = 4.6776136191489863090644121762256 absolute error = 6e-31 relative error = 1.2827053468968648615414101943930e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.54 y[1] (analytic) = 4.689098748578303052338268792909 y[1] (numeric) = 4.6890987485783030523382687929089 absolute error = 1e-31 relative error = 2.1326059731695604411445461491682e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.55 y[1] (analytic) = 4.700587048584717938495250739561 y[1] (numeric) = 4.7005870485847179384952507395605 absolute error = 5e-31 relative error = 1.0636969272817596644784178995316e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.55 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 46.81 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.56 y[1] (analytic) = 4.712078518163293660298033152513 y[1] (numeric) = 4.7120785181632936602980331525113 absolute error = 1.7e-30 relative error = 3.6077497296514440936160088290494e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.57 y[1] (analytic) = 4.723573156309729752941293880494 y[1] (numeric) = 4.723573156309729752941293880495 absolute error = 1.0e-30 relative error = 2.1170414152773395271364910111042e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.58 y[1] (analytic) = 4.73507096202036198887989724657 y[1] (numeric) = 4.7350709620203619888798972465705 absolute error = 5e-31 relative error = 1.0559503838706142605061772511600e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.59 y[1] (analytic) = 4.746571934292161773423603290526 y[1] (numeric) = 4.746571934292161773423603290524 absolute error = 2.0e-30 relative error = 4.2135672390231085715191044367876e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.6 y[1] (analytic) = 4.758076072122735541097089250916 y[1] (numeric) = 4.7580760721227355410970892509174 absolute error = 1.4e-30 relative error = 2.9423657351813073638026919344443e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.61 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.61 y[1] (analytic) = 4.769583374510324152764072349574 y[1] (numeric) = 4.7695833745103241527640723495745 absolute error = 5e-31 relative error = 1.0483095917184447766342440445156e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.62 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 19.28 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.62 y[1] (analytic) = 4.781093840453802293514325239817 y[1] (numeric) = 4.7810938404538022935143252398165 absolute error = 5e-31 relative error = 1.0457857902085059284004116167361e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.63 y[1] (analytic) = 4.792607468952677871312377773189 y[1] (numeric) = 4.7926074689526778713123777731897 absolute error = 7e-31 relative error = 1.4605827924250388649682389233330e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.64 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 18.84 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.64 y[1] (analytic) = 4.804124259007091416406701027788 y[1] (numeric) = 4.8041242590070914164067010277866 absolute error = 1.4e-30 relative error = 2.9141627579161529049048513126408e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.65 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.65 y[1] (analytic) = 4.815644209617815481498171824554 y[1] (numeric) = 4.8156442096178154814981718245543 absolute error = 3e-31 relative error = 6.2296961100415043760529236320891e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.66 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.66 y[1] (analytic) = 4.827167319786254042666618236228 y[1] (numeric) = 4.8271673197862540426666182362287 absolute error = 7e-31 relative error = 1.4501258266535410943807770795147e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.68 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.67 y[1] (analytic) = 4.838693588514441901054248866742 y[1] (numeric) = 4.8386935885144419010542488667405 absolute error = 1.5e-30 relative error = 3.1000103076593542719779169620385e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 34.83 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.68 y[1] (analytic) = 4.850223014805044085304770947121 y[1] (numeric) = 4.8502230148050440853047709471196 absolute error = 1.4e-30 relative error = 2.8864652114481654335916829652940e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.7 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 238.7 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.69 y[1] (analytic) = 4.861755597661355254757004557097 y[1] (numeric) = 4.8617555976613552547570045570975 absolute error = 5e-31 relative error = 1.0284350785558089946537234269821e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.7 y[1] (analytic) = 4.873291336087299103391802539778 y[1] (numeric) = 4.8732913360872991033918025397772 absolute error = 8e-31 relative error = 1.6416010142383758571436895749780e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.71 y[1] (analytic) = 4.884830229087427764531087929926 y[1] (numeric) = 4.8848302290874277645310879299256 absolute error = 4e-31 relative error = 8.1886162106134656394632781410012e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.72 y[1] (analytic) = 4.896372275666921216287822964655 y[1] (numeric) = 4.8963722756669212162878229646549 absolute error = 1e-31 relative error = 2.0423283682280730748975186397178e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.73 y[1] (analytic) = 4.907917474831586687765725988508 y[1] (numeric) = 4.9079174748315866877657259885087 absolute error = 7e-31 relative error = 1.4262668506340772008284901933913e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.75 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.768 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.74 y[1] (analytic) = 4.91946582558785806600755480327 y[1] (numeric) = 4.9194658255878580660075548032695 absolute error = 5e-31 relative error = 1.0163705120164176354368556853052e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop bytes used=140063152, alloc=4521156, time=5.59 x[1] = 29.75 y[1] (analytic) = 4.93101732694279530369077724617 y[1] (numeric) = 4.9310173269427953036907772461694 absolute error = 6e-31 relative error = 1.2167874501710518845556489234425e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 15.21 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.76 y[1] (analytic) = 4.942571977904083827569452008626 y[1] (numeric) = 4.9425719779040838275694520086258 absolute error = 2e-31 relative error = 4.0464762252144428985701220379581e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.77 y[1] (analytic) = 4.954129777480033947661144931151 y[1] (numeric) = 4.9541297774800339476611449311522 absolute error = 1.2e-30 relative error = 2.4222215684676544997134623016867e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.78 y[1] (analytic) = 4.965690724679580267177708228728 y[1] (numeric) = 4.9656907246795802671777082287262 absolute error = 1.8e-30 relative error = 3.6248733555917300814406532308388e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.79 y[1] (analytic) = 4.977254818512281093198752314637 y[1] (numeric) = 4.9772548185122810931987523146369 absolute error = 1e-31 relative error = 2.0091396491910042577457352550939e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.8 y[1] (analytic) = 4.988822057988317848086642099704 y[1] (numeric) = 4.9888220579883178480866420997047 absolute error = 7e-31 relative error = 1.4031368364384327891934008500578e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.81 y[1] (analytic) = 5.000392442118494481641851847771 y[1] (numeric) = 5.0003924421184944816418518477715 absolute error = 5e-31 relative error = 9.9992151773625027370867889475659e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.82 y[1] (analytic) = 5.011965969914236883997514867516 y[1] (numeric) = 5.0119659699142368839975148675152 absolute error = 8e-31 relative error = 1.5961800315529463527476675419325e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 32.02 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.83 y[1] (analytic) = 5.023542640387592299252006514963 y[1] (numeric) = 5.0235426403875922992520065149615 absolute error = 1.5e-30 relative error = 2.9859406147775173282272432740859e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 21.61 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.84 y[1] (analytic) = 5.035122452551228739838401170559 y[1] (numeric) = 5.0351224525512287398384011705571 absolute error = 1.9e-30 relative error = 3.7734931332946939291924703899872e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.85 y[1] (analytic) = 5.04670540541843440162964603935 y[1] (numeric) = 5.046705405418434401629646039349 absolute error = 1.0e-30 relative error = 1.9814907343835490057148544367286e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.86 y[1] (analytic) = 5.058291498003117079778296802692 y[1] (numeric) = 5.0582914980031170797782968026905 absolute error = 1.5e-30 relative error = 2.9654281501810666356893848000797e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.87 y[1] (analytic) = 5.069880729319803585289662324984 y[1] (numeric) = 5.0698807293198035852896623249834 absolute error = 6e-31 relative error = 1.1834597933046415291824142095264e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.91 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 47.35 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.88 y[1] (analytic) = 5.081473098383639162327207789276 y[1] (numeric) = 5.0814730983836391623272077892756 absolute error = 4e-31 relative error = 7.8717331028916715336201681431582e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.89 y[1] (analytic) = 5.09306860421038690624906780108 y[1] (numeric) = 5.09306860421038690624906780108 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.93 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.9 y[1] (analytic) = 5.10466724581642718237452316057 y[1] (numeric) = 5.1046672458164271823745231605702 absolute error = 2e-31 relative error = 3.9179830999544911760674725482963e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.94 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 5.652 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.91 y[1] (analytic) = 5.11626902221875704547929715936 y[1] (numeric) = 5.11626902221875704547929715936 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.92 y[1] (analytic) = 5.127873932434989660018529409394 y[1] (numeric) = 5.1278739324349896600185294093939 absolute error = 1e-31 relative error = 1.9501259453255442041256345487164e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.96 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.93 y[1] (analytic) = 5.139481975483353721076287358078 y[1] (numeric) = 5.1394819754833537210762873580786 absolute error = 6e-31 relative error = 1.1674328324569553522610225112487e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.94 y[1] (analytic) = 5.15109315038269287604047778568 y[1] (numeric) = 5.1510931503826928760404777856808 absolute error = 8e-31 relative error = 1.5530684005210916807274197237493e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.95 y[1] (analytic) = 5.162707456152465147002022718222 y[1] (numeric) = 5.1627074561524651470020227182213 absolute error = 7e-31 relative error = 1.3558777171574983590425649390061e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 34.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 13.44 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.96 y[1] (analytic) = 5.174324891812742353877166321615 y[1] (numeric) = 5.1743248918127423538771663216137 absolute error = 1.3e-30 relative error = 2.5124050522165137859660280891468e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 35 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.97 y[1] (analytic) = 5.185945456384209538251781470644 y[1] (numeric) = 5.1859454563842095382517814706458 absolute error = 1.8e-30 relative error = 3.4709196522383245758349679399900e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 35.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 TOP MAIN SOLVE Loop x[1] = 29.98 y[1] (analytic) = 5.197569148888164387946546809591 y[1] (numeric) = 5.1975691488881643879465468095922 absolute error = 1.2e-30 relative error = 2.3087715923061792215738710227135e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 35.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 Radius of convergence (six term test) for eq 1 = 17.11 Order of pole (six term test) = -0.5 TOP MAIN SOLVE Loop x[1] = 29.99 y[1] (analytic) = 5.20919596834651666230186723979 y[1] (numeric) = 5.2091959683465166623018672397889 absolute error = 1.1e-30 relative error = 2.1116502559782903528020083210481e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 35.04 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = ln (0.1 * x + 0.2) ; Iterations = 1000 Total Elapsed Time = 5 Seconds Elapsed Time(since restart) = 5 Seconds Time to Timeout = 2 Minutes 54 Seconds Percent Done = 100.1 % > quit bytes used=143526968, alloc=4521156, time=5.72