(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 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 , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 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"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%o3) display_poles() := block([rad_given], if glob_type_given_pole = 4 then (rad_given : sqrt(expt(array_given_rad_poles , 2.0) 1, 2 + expt(array_x - array_given_rad_poles , 2.0)), 1 1, 1 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 , 4, " ")) elseif glob_type_given_pole = 3 1, 1 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1"), if array_poles # glob_large_float then (omniout_float(ALWAYS, 1, 1 "Radius of convergence (ratio test) for eq 1 ", 4, array_poles , 4, 1, 1 " "), omniout_str(ALWAYS, "Order of pole (ratio test) Not computed")) else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1"), if (array_real_poles > 0.0) and (array_real_poles # glob_large_float) 1, 1 1, 1 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"), if (array_complex_poles > 0.0) and (array_complex_poles # 1, 1 1, 1 glob_large_float) then (omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles , 4, " "), omniout_float(ALWAYS, 1, 1 "Order of pole (six term test) ", 4, array_complex_poles , 4, " ")) else omniout_str(ALWAYS, 1, 2 "NO COMPLEX POLE (six term test) for Equation 1")) (%i4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o4) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i5) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o5) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i6) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%o6) test_suggested_h() := block([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 hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if est_tmp >= max_estimated_step_error then max_estimated_step_error : est_tmp, omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""), max_estimated_step_error) (%i7) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o7) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%o8) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 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) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 3 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "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, " ")))) (%i9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%o9) adjust_for_pole(h_param) := (block([hnew, sz2, tmp], hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > 1, 1 glob_small_float then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 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))), 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 ), hnew : sz2), return(hnew)) 1 (%i10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o10) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], 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(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 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(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 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))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i11) check_for_pole() := block([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], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) # 1, n 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()) (%o11) check_for_pole() := block([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], array_pole : glob_large_float, array_pole : glob_large_float, 1 2 tmp_rad : glob_large_float, prev_tmp_rad : glob_large_float, tmp_ratio : glob_large_float, rad_c : glob_large_float, array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, n : - 10 - 1 + glob_max_terms, cnt : 0, while (cnt < 5) and (found_sing = 1) do (if (omniabs(array_y_higher ) = 1, n 0.0) or (omniabs(array_y_higher ) = 0.0) then found_sing : 0 1, 1 + n array_y_higher glob_h 1, n tmp_rad else (tmp_rad : omniabs(-------------------------), tmp_ratio : ------------, array_y_higher prev_tmp_rad 1, 1 + n if (cnt > 0) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5) then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt = 0 then (if tmp_rad < rad_c then rad_c : tmp_rad) elseif cnt > 0 then found_sing : 0), prev_tmp_rad : tmp_rad, cnt : 1 + cnt, n : 1 + n), if found_sing = 1 then (if rad_c < array_pole 1 then (array_pole : rad_c, array_poles : rad_c)), n : glob_max_terms, 1 1, 1 m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) = 0.0) 1, m or (omniabs(array_y_higher ) = 0.0) 1, m - 1 or (omniabs(array_y_higher ) = 0.0)) do m : m - 1, 1, m - 2 array_y_higher array_y_higher 1, m 1, m - 1 if m > 10 then (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, glob_h if omniabs(hdrc) > 0.0 then (rcs : ------, hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) ord_no : -----------------------------------------------------, hdrc array_real_poles : rcs, array_real_poles : ord_no) 1, 1 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float)) 1, 2 else (array_real_poles : glob_large_float, 1, 1 array_real_poles : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) # 1, n 0.0 then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) = 0.0) rm4 rm3 rm2 or (omniabs(dr1) = 0.0) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) # 0.0 dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) # 0.0 then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_poles : rad_c, 1, 1 array_complex_poles : ord_no), if array_pole glob_ratio_of_radius < 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_poles()) (%i12) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o12) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , 1 1 1 array_tmp3 : expt(array_const_2D0 , array_tmp2 ), 1 1 1 array_tmp3_c1 : ln(array_const_2D0 ), 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_c1 array_tmp3 array_tmp2 1 1 2 array_tmp3 : --------------------------------------, 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_c1 array_tmp3 array_tmp2 1 2 2 array_tmp3 : --------------------------------------, 3 2 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_c1 array_tmp3 array_tmp2 1 3 2 array_tmp3 : --------------------------------------, 4 3 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_c1 array_tmp3 array_tmp2 1 4 2 array_tmp3 : --------------------------------------, 5 4 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk array_tmp3_c1 array_tmp3 array_tmp2 1 kkk - 1 2 --------------------------------------------, array_tmp4 : array_tmp3 , kkk - 1 kkk kkk order_d : 1, if order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o13) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , 1 1 1 array_tmp3 : expt(array_const_2D0 , array_tmp2 ), 1 1 1 array_tmp3_c1 : ln(array_const_2D0 ), 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_c1 array_tmp3 array_tmp2 1 1 2 array_tmp3 : --------------------------------------, 2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_c1 array_tmp3 array_tmp2 1 2 2 array_tmp3 : --------------------------------------, 3 2 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_c1 array_tmp3 array_tmp2 1 3 2 array_tmp3 : --------------------------------------, 4 3 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_c1 array_tmp3 array_tmp2 1 4 2 array_tmp3 : --------------------------------------, 5 4 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk array_tmp3_c1 array_tmp3 array_tmp2 1 kkk - 1 2 --------------------------------------------, array_tmp4 : array_tmp3 , kkk - 1 kkk kkk order_d : 1, if order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i14) log10(x) := --------- log(10.0) log(x) (%o14) log10(x) := --------- log(10.0) (%i15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o15) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o16) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o17) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i18) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o18) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o19) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o20) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i21) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o21) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o22) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i23) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o23) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o24) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o25) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i26) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o26) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i27) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o27) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, 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 : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), 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, " ")) (%o28) display_pole_debug(typ, m, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), 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, " ")) (%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i33) log_revs(file, revs) := printf(file, revs) (%o33) log_revs(file, revs) := printf(file, revs) (%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%o35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") elseif pole = 4 then printf(file, "Yes") else printf(file, "No"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x <= 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i56) exact_soln_y(x) := block(7.213475204444817 expt(2.0, 0.3 + 0.2 x)) (%o56) exact_soln_y(x) := block(7.213475204444817 expt(2.0, 0.3 + 0.2 x)) (%i57) main() := block([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], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/expt_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), 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:1.0,"), omniout_str(ALWAYS, "/* # did poorly with x_start := -5.0; */"), omniout_str(ALWAYS, "x_end:5.0,"), 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:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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 (x) := (block("), omniout_str(ALWAYS, " (7.2\ 134752044448170367996234050095*expt(2.0,(0.2*x+0.3))) "), 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 : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 4), array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4), array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2), array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2), array(array_type_complex_pole, 1 + 2), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_c1, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_c1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_c1 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, if glob_display_interval < glob_h then glob_h : glob_display_interval, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), 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, "2013-05-26T01:01:43-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "expt_c_lin diffeq.max"), logitem_str(html_log_file, "expt_c_lin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([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], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_yes_pole, 4, fixnum), define_variable(glob_no_pole, 3, fixnum), define_variable(glob_not_given, 0, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_estimated_step_error, 0.0, float), define_variable(glob_ratio_of_radius, 0.1, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_min_h, 1.0E-6, float), define_variable(glob_type_given_pole, 0, fixnum), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 0.0, float), define_variable(glob_smallish_float, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, 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/expt_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), 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:1.0,"), omniout_str(ALWAYS, "/* # did poorly with x_start := -5.0; */"), omniout_str(ALWAYS, "x_end:5.0,"), 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:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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 (x) := (block("), omniout_str(ALWAYS, " (7.2\ 134752044448170367996234050095*expt(2.0,(0.2*x+0.3))) "), 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 : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + 4), array(array_real_pole, 1 + 4), array(array_complex_pole, 1 + 4), array(array_1st_rel_error, 1 + 2), array(array_last_rel_error, 1 + 2), array(array_type_pole, 1 + 2), array(array_type_real_pole, 1 + 2), array(array_type_complex_pole, 1 + 2), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3_c1, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_given_rad_poles, 1 + 2, 1 + 3), array(array_given_ord_poles, 1 + 2, 1 + 3), array(array_real_poles, 1 + 2, 1 + 3), array(array_complex_poles, 1 + 2, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 4 do (array_complex_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= 2 do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_pole : 0.0, term term : 1 + term), term : 1, while term <= 2 do (array_type_real_pole : 0.0, term : 1 + term), term : 1, term while term <= 2 do (array_type_complex_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_c1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_rad_poles : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_given_ord_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_poles : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_c1 : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 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, if glob_display_interval < glob_h then glob_h : glob_display_interval, 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 (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 (found_h : true, glob_h : glob_max_h, best_h : glob_h) elseif (estimated_step_error > est_needed_step_err) glob_h and (not found_h) then (glob_h : ------, best_h : glob_h, found_h : true) 2.0 else (glob_h : glob_h 2.0, best_h : glob_h), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter), if (not found_h) and (opt_iter = 1) then (omniout_str(ALWAYS, "Beginning glob_h too large."), found_h : false), if opt_iter > 100 then (glob_h : glob_max_h, found_h : false), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_html_log then html_log_file : openw("entry.html"), if found_h then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), 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 < glob_check_sign x_end) 1 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")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), 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, "2013-05-26T01:01:43-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 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), log_revs(html_log_file, " 189 "), logitem_str(html_log_file, "expt_c_lin diffeq.max"), logitem_str(html_log_file, "expt_c_lin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/expt_c_linpostode.ode#################" "diff ( y , x , 1 ) = expt(2.0 , (0.2 * x + 0.3));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:1.0," "/* # did poorly with x_start := -5.0; */" "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (7.2134752044448170367996234050095*expt(2.0,(0.2*x+0.3))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4. "" estimated_steps = 4000000. "" step_error = 2.500000000000000000E-17 "" est_needed_step_err = 2.500000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.2339068916504653000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-204 "" estimated_step_error = 1.2339068916504653000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-204 "" best_h = 2.000000E-6 "" opt_iter = 2 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 8.28060899930145600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-197 "" estimated_step_error = 8.28060899930145600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-197 "" best_h = 4.000000E-6 "" opt_iter = 3 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.557022660245085000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-189 "" estimated_step_error = 5.557022660245085000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-189 "" best_h = 8.000000E-6 "" opt_iter = 4 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.7292548178082040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-181 "" estimated_step_error = 3.7292548178082040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-181 "" best_h = 1.600000E-5 "" opt_iter = 5 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.502660595295234000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-173 "" estimated_step_error = 2.502660595295234000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-173 "" best_h = 3.200000E-5 "" opt_iter = 6 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.6795071642646808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-165 "" estimated_step_error = 1.6795071642646808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-165 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.12709827132864660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-157 "" estimated_step_error = 1.12709827132864660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-157 "" best_h = 1.280000E-4 "" opt_iter = 8 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 7.563829703272082000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 "" estimated_step_error = 7.563829703272082000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-150 "" best_h = 2.560000E-4 "" opt_iter = 9 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 5.076001856750940000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 "" estimated_step_error = 5.076001856750940000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-142 "" best_h = 5.120000E-4 "" opt_iter = 10 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.406449421425509000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-134 "" estimated_step_error = 3.406449421425509000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-134 "" best_h = 1.024000E-3 "" opt_iter = 11 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.2860325142463137000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-126 "" estimated_step_error = 2.2860325142463137000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-126 "" best_h = 2.048000E-3 "" opt_iter = 12 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.5341344839616788000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-118 "" estimated_step_error = 1.5341344839616788000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-118 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.029545637434692200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-110 "" estimated_step_error = 1.029545637434692200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-110 "" best_h = 8.192000E-3 "" opt_iter = 14 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 6.9092364698123250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" estimated_step_error = 6.9092364698123250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-103 "" best_h = 1.638400E-2 "" opt_iter = 15 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.63680762263686900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-95 "" estimated_step_error = 4.63680762263686900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-95 "" best_h = 3.276800E-2 "" opt_iter = 16 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 3.111839814041088000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 "" estimated_step_error = 3.111839814041088000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-87 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.08849605118259950000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 "" estimated_step_error = 2.08849605118259950000000000000000000000000000000000000000000000000000000000000000000000000000000E-79 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.401801855884818300000000000000000000000000000000000000000000000000000000000000000000000E-71 "" estimated_step_error = 1.401801855884818300000000000000000000000000000000000000000000000000000000000000000000000E-71 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1. " " y[1] (analytic) = 10.201394465967896 " " y[1] (numeric) = 10.201394465967896 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643046 " " Order of pole (six term test) = 66094165532996. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.01 " " y[1] (analytic) = 10.215546408704384 " " y[1] (numeric) = 10.215546408704386 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.73887599187711200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013485 " " Order of pole (six term test) = 198282496599010.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.02 " " y[1] (analytic) = 10.229717983804264 " " y[1] (numeric) = 10.229717983804264 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 495095928.1979421 " " Order of pole (six term test) = -41743683494542.42 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.03 " " y[1] (analytic) = 10.243909218502639 " " y[1] (numeric) = 10.243909218502639 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 91.58934435839139 " " Order of pole (six term test) = -198282496599033.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.04 " " y[1] (analytic) = 10.258120140072398 " " y[1] (numeric) = 10.258120140072398 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.05 " " y[1] (analytic) = 10.272350775824268 " " y[1] (numeric) = 10.27235077582427 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.729260300943834500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.06 " " y[1] (analytic) = 10.286601153106863 " " y[1] (numeric) = 10.286601153106863 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.90135 " " Order of pole (six term test) = -396564993198060. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.07 " " y[1] (analytic) = 10.300871299306731 " " y[1] (numeric) = 10.300871299306731 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.08 " " y[1] (analytic) = 10.315161241848417 " " y[1] (numeric) = 10.315161241848417 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 435996610.3709041 " " Order of pole (six term test) = 28326070942705.844 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.09 " " y[1] (analytic) = 10.329471008194506 " " y[1] (numeric) = 10.329471008194508 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.719697783159508400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 462444239.6514238 " " Order of pole (six term test) = -14163035471370.572 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1 " " y[1] (analytic) = 10.34380062584569 " " y[1] (numeric) = 10.34380062584569 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 557212083.1571808 " " Order of pole (six term test) = -66094165533018.664 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.11 " " y[1] (analytic) = 10.358150122340799 " " y[1] (numeric) = 10.3581501223408 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.714936372247536400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 257939073.2115244 " " Order of pole (six term test) = 118969497959402.4 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.12 " " y[1] (analytic) = 10.372519525256877 " " y[1] (numeric) = 10.372519525256878 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.712560612756483200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = 33047082766492.33 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000001 " " y[1] (analytic) = 10.386908862209218 " " y[1] (numeric) = 10.38690886220922 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.710188144485589300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.4230531 " " Order of pole (six term test) = 39656499319792.72 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000001 " " y[1] (analytic) = 10.40131816085143 " " y[1] (numeric) = 10.40131816085143 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000001 " " y[1] (analytic) = 10.415747448875479 " " y[1] (numeric) = 10.415747448875479 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 482559819.3097667 " " Order of pole (six term test) = -49570624149768. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000001 " " y[1] (analytic) = 10.43019675401175 " " y[1] (numeric) = 10.43019675401175 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000002 " " y[1] (analytic) = 10.444666104029094 " " y[1] (numeric) = 10.444666104029094 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000002 " " y[1] (analytic) = 10.459155526734891 " " y[1] (numeric) = 10.459155526734891 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000002 " " y[1] (analytic) = 10.47366504997509 " " y[1] (numeric) = 10.473665049975091 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.696022195596636500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000002 " " y[1] (analytic) = 10.488194701634274 " " y[1] (numeric) = 10.488194701634274 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000002 " " y[1] (analytic) = 10.502744509635704 " " y[1] (numeric) = 10.502744509635704 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643046 " " Order of pole (six term test) = -11. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000002 " " y[1] (analytic) = 10.517314501941383 " " y[1] (numeric) = 10.517314501941383 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -297423744898547. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000002 " " y[1] (analytic) = 10.531904706552103 " " y[1] (numeric) = 10.531904706552103 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000002 " " y[1] (analytic) = 10.546515151507498 " " y[1] (numeric) = 10.546515151507498 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844516 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542715 " " Order of pole (six term test) = -49570624149767.875 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000002 " " y[1] (analytic) = 10.561145864886104 " " y[1] (numeric) = 10.561145864886102 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.68197358707667780000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 616592319.5352314 " " Order of pole (six term test) = -141630354713600.16 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2600000000000002 " " y[1] (analytic) = 10.575796874805404 " " y[1] (numeric) = 10.575796874805402 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.679643492049327000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2700000000000002 " " y[1] (analytic) = 10.590468209421891 " " y[1] (numeric) = 10.59046820942189 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.677316624981604600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2800000000000002 " " y[1] (analytic) = 10.605159896931118 " " y[1] (numeric) = 10.605159896931116 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6749929814017100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2900000000000003 " " y[1] (analytic) = 10.619871965567752 " " y[1] (numeric) = 10.61987196556775 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.672672556844035700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.3000000000000003 " " y[1] (analytic) = 10.634604443605626 " " y[1] (numeric) = 10.634604443605625 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.67035534684916100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013458 " " Order of pole (six term test) = -594847489797079. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3100000000000003 " " y[1] (analytic) = 10.649357359357802 " " y[1] (numeric) = 10.6493573593578 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.66804134696384300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.3200000000000003 " " y[1] (analytic) = 10.664130741176614 " " y[1] (numeric) = 10.664130741176612 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.665730552741008800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.3300000000000003 " " y[1] (analytic) = 10.678924617453731 " " y[1] (numeric) = 10.678924617453728 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.326845919479489000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085394 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3400000000000003 " " y[1] (analytic) = 10.693739016620203 " " y[1] (numeric) = 10.693739016620201 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.661118563525290600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -693988738096594.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3500000000000003 " " y[1] (analytic) = 10.708573967146531 " " y[1] (numeric) = 10.708573967146528 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.31763471933805730000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.3600000000000003 " " y[1] (analytic) = 10.723429497542703 " " y[1] (numeric) = 10.7234294975427 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.31303868749695500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1823904678.008439 " " Order of pole (six term test) = -1586259972792192.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3700000000000003 " " y[1] (analytic) = 10.738305636358263 " " y[1] (numeric) = 10.738305636358259 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.30844902269456300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.3800000000000003 " " y[1] (analytic) = 10.753202412182356 " " y[1] (numeric) = 10.753202412182352 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.303865716110406000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013561 " " Order of pole (six term test) = -9. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.3900000000000003 " " y[1] (analytic) = 10.768119853643793 " " y[1] (numeric) = 10.768119853643789 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.2992887589362300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -99141248299523. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4000000000000004 " " y[1] (analytic) = 10.783057989411095 " " y[1] (numeric) = 10.783057989411091 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.29471814237598200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 607968226.0028149 " " Order of pole (six term test) = -44062777022017.39 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4100000000000004 " " y[1] (analytic) = 10.798016848192557 " " y[1] (numeric) = 10.798016848192553 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.290153857645793400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 446763580.05959237 " " Order of pole (six term test) = 39656499319792.81 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4200000000000004 " " y[1] (analytic) = 10.812996458736299 " " y[1] (numeric) = 10.812996458736295 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.28559589597396560000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085409 " " Order of pole (six term test) = -991412482995130.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4300000000000004 " " y[1] (analytic) = 10.82799684983032 " " y[1] (numeric) = 10.827996849830317 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.28104424860095300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4400000000000004 " " y[1] (analytic) = 10.84301805030256 " " y[1] (numeric) = 10.843018050302556 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.27649890677934200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.4500000000000004 " " y[1] (analytic) = 10.858060089020945 " " y[1] (numeric) = 10.858060089020942 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.27195986177383900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013485 " " Order of pole (six term test) = -12.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4600000000000004 " " y[1] (analytic) = 10.873122994893453 " " y[1] (numeric) = 10.87312299489345 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.26742710486125100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -495706241497571. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4700000000000004 " " y[1] (analytic) = 10.888206796868161 " " y[1] (numeric) = 10.88820679686816 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.63145031366523500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.4800000000000004 " " y[1] (analytic) = 10.903311523933308 " " y[1] (numeric) = 10.903311523933306 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.629190210241227600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 452455065.3055835 " " Order of pole (six term test) = -45757499215171.66 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.4900000000000004 " " y[1] (analytic) = 10.918437205117344 " " y[1] (numeric) = 10.918437205117343 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.626933237815108300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5000000000000004 " " y[1] (analytic) = 10.933583869488992 " " y[1] (numeric) = 10.93358386948899 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.624679392049400400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562788 " " Order of pole (six term test) = 66094165532995.84 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000005 " " y[1] (analytic) = 10.948751546157293 " " y[1] (numeric) = 10.948751546157293 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000005 " " y[1] (analytic) = 10.963940264271683 " " y[1] (numeric) = 10.963940264271683 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085409 " " Order of pole (six term test) = -991412482995130.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000005 " " y[1] (analytic) = 10.979150053022027 " " y[1] (numeric) = 10.979150053022025 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.617936571430049800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000005 " " y[1] (analytic) = 10.99438094163868 " " y[1] (numeric) = 10.994380941638678 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.615695189051262500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643124 " " Order of pole (six term test) = 66094165532996.875 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000005 " " y[1] (analytic) = 11.009632959392555 " " y[1] (numeric) = 11.009632959392553 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.613456911735465200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 549927951.8480003 " " Order of pole (six term test) = -126179770563027.45 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000005 " " y[1] (analytic) = 11.02490613559517 " " y[1] (numeric) = 11.024906135595167 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.22244347036221800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 719357706.124438 " " Order of pole (six term test) = -242345273621041.06 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000005 " " y[1] (analytic) = 11.0402004995987 " " y[1] (numeric) = 11.040200499598699 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.608989655092603600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085373 " " Order of pole (six term test) = -892271234695613.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000005 " " y[1] (analytic) = 11.055516080796046 " " y[1] (numeric) = 11.055516080796046 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000005 " " y[1] (analytic) = 11.070852908620882 " " y[1] (numeric) = 11.070852908620882 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901348 " " Order of pole (six term test) = -12.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000005 " " y[1] (analytic) = 11.086211012547711 " " y[1] (numeric) = 11.086211012547711 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1053031856.8243932 " " Order of pole (six term test) = -264376662132043.84 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000005 " " y[1] (analytic) = 11.101590422091927 " " y[1] (numeric) = 11.101590422091927 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000006 " " y[1] (analytic) = 11.116991166809871 " " y[1] (numeric) = 11.116991166809871 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000006 " " y[1] (analytic) = 11.132413276298884 " " y[1] (numeric) = 11.132413276298884 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000006 " " y[1] (analytic) = 11.147856780197365 " " y[1] (numeric) = 11.147856780197365 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000006 " " y[1] (analytic) = 11.163321708184835 " " y[1] (numeric) = 11.163321708184833 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.59124397364437100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013458 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000006 " " y[1] (analytic) = 11.178808089981978 " " y[1] (numeric) = 11.178808089981978 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996482 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000006 " " y[1] (analytic) = 11.194315955350719 " " y[1] (numeric) = 11.194315955350717 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.586838219043815700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000006 " " y[1] (analytic) = 11.209845334094263 " " y[1] (numeric) = 11.209845334094261 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.584639918266791400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 491870513.22373986 " " Order of pole (six term test) = -162231133581030.34 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000006 " " y[1] (analytic) = 11.225396256057161 " " y[1] (numeric) = 11.22539625605716 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.582444662870353700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.8664309 " " Order of pole (six term test) = -132188331066027.12 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000006 " " y[1] (analytic) = 11.240968751125369 " " y[1] (numeric) = 11.240968751125369 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 616592319.5352283 " " Order of pole (six term test) = 28326070942706.156 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000006 " " y[1] (analytic) = 11.256562849226302 " " y[1] (numeric) = 11.2565628492263 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.578063271349606200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000006 " " y[1] (analytic) = 11.272178580328887 " " y[1] (numeric) = 11.272178580328886 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.575877126805084700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000006 " " y[1] (analytic) = 11.28781597444363 " " y[1] (numeric) = 11.28781597444363 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1289695366.0576336 " " Order of pole (six term test) = -1090553731294636.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000007 " " y[1] (analytic) = 11.30347506162267 " " y[1] (numeric) = 11.30347506162267 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000007 " " y[1] (analytic) = 11.319155871959834 " " y[1] (numeric) = 11.319155871959834 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542682 " " Order of pole (six term test) = -99141248299523.7 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000007 " " y[1] (analytic) = 11.334858435590697 " " y[1] (numeric) = 11.334858435590697 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000007 " " y[1] (analytic) = 11.350582782692637 " " y[1] (numeric) = 11.350582782692639 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.56499174836100820000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000007 " " y[1] (analytic) = 11.366328943484904 " " y[1] (numeric) = 11.366328943484904 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000007 " " y[1] (analytic) = 11.382096948228659 " " y[1] (numeric) = 11.38209694822866 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.56065867957371100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643404 " " Order of pole (six term test) = -462659158731068. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000007 " " y[1] (analytic) = 11.397886827227053 " " y[1] (numeric) = 11.397886827227055 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.55849664620017430000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000007 " " y[1] (analytic) = 11.413698610825268 " " y[1] (numeric) = 11.41369861082527 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.556337607964760300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 533984612.4958798 " " Order of pole (six term test) = 56652141885423.60 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000007 " " y[1] (analytic) = 11.429532329410588 " " y[1] (numeric) = 11.429532329410588 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000007 " " y[1] (analytic) = 11.445388013412444 " " y[1] (numeric) = 11.445388013412446 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.552028500316984500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000007 " " y[1] (analytic) = 11.46126569330249 " " y[1] (numeric) = 11.461265693302492 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.54987842262332610000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000008 " " y[1] (analytic) = 11.477165399594647 " " y[1] (numeric) = 11.477165399594648 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.54773132350518200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000008 " " y[1] (analytic) = 11.493087162845166 " " y[1] (numeric) = 11.493087162845168 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.54558719883623100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901349 " " Order of pole (six term test) = -396564993198058.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000008 " " y[1] (analytic) = 11.509031013652688 " " y[1] (numeric) = 11.50903101365269 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.543446044495867500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 998993734.8844213 " " Order of pole (six term test) = -396564993198059. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000008 " " y[1] (analytic) = 11.524996982658305 " " y[1] (numeric) = 11.524996982658307 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.541307856369194300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000008 " " y[1] (analytic) = 11.54098510054561 " " y[1] (numeric) = 11.540985100545612 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.539172630347015700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000008 " " y[1] (analytic) = 11.556995398040769 " " y[1] (numeric) = 11.55699539804077 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.537040362325827500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000008 " " y[1] (analytic) = 11.573027905912568 " " y[1] (numeric) = 11.57302790591257 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.534911048207810700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1289695366.0576403 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000008 " " y[1] (analytic) = 11.589082654972477 " " y[1] (numeric) = 11.589082654972481 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.06556936780164660000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000008 " " y[1] (analytic) = 11.605159676074718 " " y[1] (numeric) = 11.60515967607472 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.530661265318391800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = -33047082766515.164 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000008 " " y[1] (analytic) = 11.621259000116302 " " y[1] (numeric) = 11.621259000116304 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.52854078837970400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000008 " " y[1] (analytic) = 11.637380658037111 " " y[1] (numeric) = 11.637380658037113 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.526423249009601600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000009 " " y[1] (analytic) = 11.653524680819945 " " y[1] (numeric) = 11.653524680819949 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.04861728627714270000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643213 " " Order of pole (six term test) = 66094165532995.84 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000009 " " y[1] (analytic) = 11.669691099490592 " " y[1] (numeric) = 11.669691099490594 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.522196966702736900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000009 " " y[1] (analytic) = 11.68587994511787 " " y[1] (numeric) = 11.685879945117872 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.520088215643852800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 549927951.8479986 " " Order of pole (six term test) = -54077044527017.68 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000009 " " y[1] (analytic) = 11.702091248813705 " " y[1] (numeric) = 11.702091248813707 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.517982385909294700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 557212083.1571835 " " Order of pole (six term test) = -118969497959426.3 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.000000000000001 " " y[1] (analytic) = 11.718325041733179 " " y[1] (numeric) = 11.71832504173318 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.515879473452053600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0100000000000007 " " y[1] (analytic) = 11.734581355074598 " " y[1] (numeric) = 11.7345813550746 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.51377947423072600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0200000000000005 " " y[1] (analytic) = 11.750860220079545 " " y[1] (numeric) = 11.750860220079547 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.511682384209507600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000002 " " y[1] (analytic) = 11.767161668032943 " " y[1] (numeric) = 11.767161668032946 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.0191763987163700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.04 " " y[1] (analytic) = 11.783485730263118 " " y[1] (numeric) = 11.783485730263122 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.014993831304254600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 631819114.0946314 " " Order of pole (six term test) = -79312998639619.4 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.05 " " y[1] (analytic) = 11.799832438141854 " " y[1] (numeric) = 11.799832438141857 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.0108170581445600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0599999999999996 " " y[1] (analytic) = 11.816201823084457 " " y[1] (numeric) = 11.81620182308446 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.00664607121031200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542701 " " Order of pole (six term test) = -99141248299523. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0699999999999994 " " y[1] (analytic) = 11.832593916549813 " " y[1] (numeric) = 11.832593916549817 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 3.00248086248565600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.079999999999999 " " y[1] (analytic) = 11.849008750040447 " " y[1] (numeric) = 11.849008750040452 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.49748213594876500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.089999999999999 " " y[1] (analytic) = 11.865446355102591 " " y[1] (numeric) = 11.865446355102598 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.98833549531442500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0999999999999988 " " y[1] (analytic) = 11.881906763326242 " " y[1] (numeric) = 11.881906763326247 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.48502973836576500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1099999999999985 " " y[1] (analytic) = 11.898390006345211 " " y[1] (numeric) = 11.898390006345217 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 4.47881647463131360000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999983 " " y[1] (analytic) = 11.914896115837198 " " y[1] (numeric) = 11.914896115837205 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.9634824244556500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901349 " " Order of pole (six term test) = -297423744898547.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.129999999999998 " " y[1] (analytic) = 11.931425123523852 " " y[1] (numeric) = 11.931425123523859 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 5.95522101009713400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.139999999999998 " " y[1] (analytic) = 11.947977061170818 " " y[1] (numeric) = 11.947977061170828 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.92045656083397300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1499999999999977 " " y[1] (analytic) = 11.964551960587823 " " y[1] (numeric) = 11.964551960587832 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 7.42341562497162400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1599999999999975 " " y[1] (analytic) = 11.981149853628706 " " y[1] (numeric) = 11.981149853628716 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.89575805879224000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1289695366.0576377 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999973 " " y[1] (analytic) = 11.997770772191508 " " y[1] (numeric) = 11.997770772191517 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 7.40286205299695800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.179999999999997 " " y[1] (analytic) = 12.014414748218512 " " y[1] (numeric) = 12.014414748218522 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.87112794069464300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.189999999999997 " " y[1] (analytic) = 12.03108181369632 " " y[1] (numeric) = 12.03108181369633 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.85883846643628800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1079036559.1866527 " " Order of pole (six term test) = -396564993198056. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1999999999999966 " " y[1] (analytic) = 12.0477720006559 " " y[1] (numeric) = 12.047772000655913 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.03209936867370980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2099999999999964 " " y[1] (analytic) = 12.064485341172666 " " y[1] (numeric) = 12.064485341172679 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.03066956643117960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.219999999999996 " " y[1] (analytic) = 12.081221867366521 " " y[1] (numeric) = 12.081221867366532 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 8.82207209950426800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 257939073.2115231 " " Order of pole (six term test) = 118969497959403.2 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.229999999999996 " " y[1] (analytic) = 12.097981611401924 " " y[1] (numeric) = 12.097981611401936 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.027815901462660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2399999999999958 " " y[1] (analytic) = 12.11476460548796 " " y[1] (numeric) = 12.114764605487974 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.1730194665742429000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = -33047082766515.164 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2499999999999956 " " y[1] (analytic) = 12.131570881878398 " " y[1] (numeric) = 12.13157088187841 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.02497013757516400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 689371170.4425275 " " Order of pole (six term test) = -254934638484472. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2599999999999953 " " y[1] (analytic) = 12.148400472871742 " " y[1] (numeric) = 12.148400472871757 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.16977167051216930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.75427 " " Order of pole (six term test) = -11.296875 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.269999999999995 " " y[1] (analytic) = 12.165253410811314 " " y[1] (numeric) = 12.165253410811326 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.02213225289258340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.279999999999995 " " y[1] (analytic) = 12.182129728085291 " " y[1] (numeric) = 12.182129728085306 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.16653286678105120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.508543 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2899999999999947 " " y[1] (analytic) = 12.199029457126795 " " y[1] (numeric) = 12.19902945712681 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.31053143291349040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.90135 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2999999999999945 " " y[1] (analytic) = 12.215952630413932 " " y[1] (numeric) = 12.215952630413948 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.3087159092938080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999943 " " y[1] (analytic) = 12.232899280469868 " " y[1] (numeric) = 12.232899280469882 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.16169146736048030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.319999999999994 " " y[1] (analytic) = 12.249869439862879 " " y[1] (numeric) = 12.249869439862893 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.16008213679060040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 508662712.09938926 " " Order of pole (six term test) = -55078471277518.61 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.329999999999994 " " y[1] (analytic) = 12.26686314120643 " " y[1] (numeric) = 12.266863141206445 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.15847503568091360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3399999999999936 " " y[1] (analytic) = 12.283880417159226 " " y[1] (numeric) = 12.283880417159242 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.30147893106073250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013436 " " Order of pole (six term test) = -11.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3499999999999934 " " y[1] (analytic) = 12.300921300425282 " " y[1] (numeric) = 12.300921300425296 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.15526750949221090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -297423744898546. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.359999999999993 " " y[1] (analytic) = 12.317985823753972 " " y[1] (numeric) = 12.317985823753988 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.2978754630300480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 407837484.45067084 " " Order of pole (six term test) = -82617706916271.67 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.369999999999993 " " y[1] (analytic) = 12.335074019940114 " " y[1] (numeric) = 12.335074019940128 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.15206886413730630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 407837484.4506729 " " Order of pole (six term test) = -148711872449279.16 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.379999999999993 " " y[1] (analytic) = 12.352185921824008 " " y[1] (numeric) = 12.352185921824024 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.29428197209660150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 631819114.0946347 " " Order of pole (six term test) = -158625997279230.9 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3899999999999926 " " y[1] (analytic) = 12.369321562291523 " " y[1] (numeric) = 12.36932156229154 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.43609884378425450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3999999999999924 " " y[1] (analytic) = 12.386480974274146 " " y[1] (numeric) = 12.386480974274162 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.29069843063631840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.4230547 " " Order of pole (six term test) = -19828249659914.594 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.409999999999992 " " y[1] (analytic) = 12.403664190749044 " " y[1] (numeric) = 12.40366419074906 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.2889103823470090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.419999999999992 " " y[1] (analytic) = 12.420871244739137 " " y[1] (numeric) = 12.420871244739152 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.1441109432014292000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.44220984 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4299999999999917 " " y[1] (analytic) = 12.43810216931315 " " y[1] (numeric) = 12.438102169313167 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.28534171346858200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4399999999999915 " " y[1] (analytic) = 12.455356997585692 " " y[1] (numeric) = 12.455356997585708 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.28356108602115240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999913 " " y[1] (analytic) = 12.472635762717305 " " y[1] (numeric) = 12.472635762717319 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 1.1393626002998108000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 762994068.1490847 " " Order of pole (six term test) = -123926560374401.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.459999999999991 " " y[1] (analytic) = 12.489938497914528 " " y[1] (numeric) = 12.489938497914544 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.28000722799969550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.42305595 " " Order of pole (six term test) = -19828249659914.203 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.469999999999991 " " y[1] (analytic) = 12.507265236429976 " " y[1] (numeric) = 12.507265236429992 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.27823399059581950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4799999999999907 " " y[1] (analytic) = 12.524616011562388 " " y[1] (numeric) = 12.524616011562406 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.41829245524203340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4899999999999904 " " y[1] (analytic) = 12.541990856656701 " " y[1] (numeric) = 12.541990856656717 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.27469488196261860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999902 " " y[1] (analytic) = 12.559389805104102 " " y[1] (numeric) = 12.55938980510412 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.41436555992421220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.50999999999999 " " y[1] (analytic) = 12.57681289034211 " " y[1] (numeric) = 12.576812890342127 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.4124061913685118000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.508543 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.51999999999999 " " y[1] (analytic) = 12.594260145854623 " " y[1] (numeric) = 12.59426014585464 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.41044953719249240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5299999999999896 " " y[1] (analytic) = 12.611731605171991 " " y[1] (numeric) = 12.611731605172011 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.54934515299941480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5399999999999894 " " y[1] (analytic) = 12.629227301871085 " " y[1] (numeric) = 12.629227301871104 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 1.54719879263775800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.549999999999989 " " y[1] (analytic) = 12.646747269575346 " " y[1] (numeric) = 12.646747269575368 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.68551498803840380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.559999999999989 " " y[1] (analytic) = 12.664291541954869 " " y[1] (numeric) = 12.66429154195489 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.68317998698825050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5699999999999887 " " y[1] (analytic) = 12.681860152726452 " " y[1] (numeric) = 12.681860152726474 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 1.68084822069420580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643195 " " Order of pole (six term test) = 66094165532995.66 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5799999999999885 " " y[1] (analytic) = 12.699453135653664 " " y[1] (numeric) = 12.69945313565369 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.9582729654542289000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999883 " " y[1] (analytic) = 12.717070524546926 " " y[1] (numeric) = 12.71707052454695 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.81587723899376440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.599999999999988 " " y[1] (analytic) = 12.734712353263548 " " y[1] (numeric) = 12.734712353263571 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.81336164269821630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.609999999999988 " " y[1] (analytic) = 12.752378655707815 " " y[1] (numeric) = 12.752378655707838 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.81084953134349250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6199999999999877 " " y[1] (analytic) = 12.770069465831046 " " y[1] (numeric) = 12.77006946583107 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.80834090010178670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013463 " " Order of pole (six term test) = 198282496599010.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6299999999999875 " " y[1] (analytic) = 12.787784817631657 " " y[1] (numeric) = 12.787784817631682 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.94474618600982470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = 33047082766491.67 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999872 " " y[1] (analytic) = 12.805524745155234 " " y[1] (numeric) = 12.805524745155259 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.94205206319345070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.649999999999987 " " y[1] (analytic) = 12.823289282494587 " " y[1] (numeric) = 12.82328928249461 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.80083583887697430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1079036559.18665 " " Order of pole (six term test) = -396564993198054. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.659999999999987 " " y[1] (analytic) = 12.841078463789822 " " y[1] (numeric) = 12.841078463789845 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.79834107994289620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 64.76344648024842 " " Order of pole (six term test) = -198282496599034.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6699999999999866 " " y[1] (analytic) = 12.858892323228408 " " y[1] (numeric) = 12.858892323228432 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 1.79584977708293930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6799999999999864 " " y[1] (analytic) = 12.876730895045242 " " y[1] (numeric) = 12.876730895045267 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.93131284285615500000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 998993734.884418 " " Order of pole (six term test) = -198282496599034. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.689999999999986 " " y[1] (analytic) = 12.89459421352271 " " y[1] (numeric) = 12.894594213522735 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.92863732970542820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 288384650.87713176 " " Order of pole (six term test) = -148711872449278.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.699999999999986 " " y[1] (analytic) = 12.912482312990761 " " y[1] (numeric) = 12.912482312990786 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.92596552303376600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542701 " " Order of pole (six term test) = -148711872449278.87 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7099999999999858 " " y[1] (analytic) = 12.930395227826963 " " y[1] (numeric) = 12.930395227826988 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 1.9232974177064580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7199999999999855 " " y[1] (analytic) = 12.948332992456578 " " y[1] (numeric) = 12.948332992456605 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.05782108063847060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901351 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999853 " " y[1] (analytic) = 12.966295641352623 " " y[1] (numeric) = 12.966295641352652 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.19196833209327480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643404 " " Order of pole (six term test) = -396564993198060. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.739999999999985 " " y[1] (analytic) = 12.984283209035944 " " y[1] (numeric) = 12.98428320903597 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.052123491303769800000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643165 " " Order of pole (six term test) = -231329579365538.7 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.749999999999985 " " y[1] (analytic) = 13.002295730075263 " " y[1] (numeric) = 13.002295730075291 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.18589932273748480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7599999999999847 " " y[1] (analytic) = 13.02033323908727 " " y[1] (numeric) = 13.020333239087298 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.18287112230595880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562802 " " Order of pole (six term test) = -66094165533020.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7699999999999845 " " y[1] (analytic) = 13.038395770736674 " " y[1] (numeric) = 13.0383957707367 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 2.04360667213419670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999843 " " y[1] (analytic) = 13.056483359736264 " " y[1] (numeric) = 13.056483359736296 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 2.44893071344215150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.789999999999984 " " y[1] (analytic) = 13.074596040847004 " " y[1] (numeric) = 13.074596040847034 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 2.30967489744700020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.799999999999984 " " y[1] (analytic) = 13.092733848878062 " " y[1] (numeric) = 13.09273384887809 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.17080021319149550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 64.76344648024842 " " Order of pole (six term test) = -198282496599034.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8099999999999836 " " y[1] (analytic) = 13.1108968186869 " " y[1] (numeric) = 13.11089681868693 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 2.30327998819753470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8199999999999834 " " y[1] (analytic) = 13.129084985179341 " " y[1] (numeric) = 13.129084985179372 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 2.30008917635106280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 407837484.4506729 " " Order of pole (six term test) = -198282496599035. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.829999999999983 " " y[1] (analytic) = 13.147298383309623 " " y[1] (numeric) = 13.147298383309659 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.7022385704051860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.90135 " " Order of pole (six term test) = -396564993198060. " " " " "TOP MAIN SOLVE Loop" x[1] = 2.839999999999983 " " y[1] (analytic) = 13.16553704808049 " " y[1] (numeric) = 13.165537048080525 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.69849506771049630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 616592319.5352283 " " Order of pole (six term test) = 28326070942706.156 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8499999999999828 " " y[1] (analytic) = 13.183801014543226 " " y[1] (numeric) = 13.183801014543262 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.69475675101699060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8599999999999826 " " y[1] (analytic) = 13.20209031779775 " " y[1] (numeric) = 13.202090317797785 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 2.5564724324833094000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8699999999999823 " " y[1] (analytic) = 13.220404992992668 " " y[1] (numeric) = 13.220404992992703 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.6872956469061110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.879999999999982 " " y[1] (analytic) = 13.238745075325353 " " y[1] (numeric) = 13.238745075325388 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.68357284514989400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.889999999999982 " " y[1] (analytic) = 13.257110600041997 " " y[1] (numeric) = 13.257110600042035 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.8138479607530076000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8999999999999817 " " y[1] (analytic) = 13.2755016024377 " " y[1] (numeric) = 13.275501602437737 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.8099498417864260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9099999999999815 " " y[1] (analytic) = 13.293918117856514 " " y[1] (numeric) = 13.293918117856549 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.6724353552535150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999813 " " y[1] (analytic) = 13.312360181691524 " " y[1] (numeric) = 13.31236018169156 " " absolute error = 3.55271367880050100000000000000E-14 " " relative error = 2.6687331399630730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1053031856.8243942 " " Order of pole (six term test) = -396564993198060.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.929999999999981 " " y[1] (analytic) = 13.330827829384914 " " y[1] (numeric) = 13.330827829384953 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.9315396588246734000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.939999999999981 " " y[1] (analytic) = 13.349321096428046 " " y[1] (numeric) = 13.349321096428085 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.9274784975591250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9499999999999806 " " y[1] (analytic) = 13.367840018361504 " " y[1] (numeric) = 13.367840018361543 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.9234229623579480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9599999999999804 " " y[1] (analytic) = 13.386384630775183 " " y[1] (numeric) = 13.38638463077522 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.7866742706350190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.96999999999998 " " y[1] (analytic) = 13.404954969308346 " " y[1] (numeric) = 13.404954969308383 " " absolute error = 3.73034936274052600000000000000E-14 " " relative error = 2.7828137963025180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.97999999999998 " " y[1] (analytic) = 13.4235510696497 " " y[1] (numeric) = 13.423551069649738 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.9112900352548320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013497 " " Order of pole (six term test) = -12.09375 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.98999999999998 " " y[1] (analytic) = 13.442172967537461 " " y[1] (numeric) = 13.4421729675375 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.90725692647925700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643237 " " Order of pole (six term test) = -66094165533019.88 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9999999999999796 " " y[1] (analytic) = 13.460820698759424 " " y[1] (numeric) = 13.460820698759463 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.90322940490598650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013485 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0099999999999794 " " y[1] (analytic) = 13.479494299153027 " " y[1] (numeric) = 13.479494299153068 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.03098962019464850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 446763580.05959237 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.019999999999979 " " y[1] (analytic) = 13.49819380460543 " " y[1] (numeric) = 13.498193804605469 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.8951910924165214000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 495095928.1979445 " " Order of pole (six term test) = -104359208736339.6 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.029999999999979 " " y[1] (analytic) = 13.516919251053569 " " y[1] (numeric) = 13.516919251053608 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.89118028605219730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0399999999999787 " " y[1] (analytic) = 13.535670674484239 " " y[1] (numeric) = 13.53567067448428 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.0184102649027060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0499999999999785 " " y[1] (analytic) = 13.554448110934162 " " y[1] (numeric) = 13.554448110934201 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.8831753345442673000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999783 " " y[1] (analytic) = 13.57325159649004 " " y[1] (numeric) = 13.573251596490081 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.0100530455628570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643136 " " Order of pole (six term test) = -44062777022016.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.069999999999978 " " y[1] (analytic) = 13.592081167288653 " " y[1] (numeric) = 13.592081167288693 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.0058831170411376000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.079999999999978 " " y[1] (analytic) = 13.610936859516896 " " y[1] (numeric) = 13.610936859516936 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 3.00171896526275600000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0899999999999777 " " y[1] (analytic) = 13.629818709411872 " " y[1] (numeric) = 13.629818709411914 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.12788930319129740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0999999999999774 " " y[1] (analytic) = 13.648726753260958 " " y[1] (numeric) = 13.648726753261 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.1235561321073580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999772 " " y[1] (analytic) = 13.667661027401865 " " y[1] (numeric) = 13.667661027401905 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 2.9892610904158680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.119999999999977 " " y[1] (analytic) = 13.686621568222714 " " y[1] (numeric) = 13.686621568222753 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 2.8553321410990290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996492 " " Order of pole (six term test) = -396564993198058.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.129999999999977 " " y[1] (analytic) = 13.705608412162103 " " y[1] (numeric) = 13.705608412162144 " " absolute error = 4.08562073062057600000000000000E-14 " " relative error = 2.98098457781346750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1399999999999766 " " y[1] (analytic) = 13.724621595709188 " " y[1] (numeric) = 13.72462159570923 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.10628339355705800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1499999999999764 " " y[1] (analytic) = 13.743661155403741 " " y[1] (numeric) = 13.743661155403784 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.10198015387215140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.4230524 " " Order of pole (six term test) = -66094165533018.664 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.159999999999976 " " y[1] (analytic) = 13.762727127836222 " " y[1] (numeric) = 13.762727127836264 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.0976828756110570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996482 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.169999999999976 " " y[1] (analytic) = 13.78181954964785 " " y[1] (numeric) = 13.781819549647894 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 3.22228286512001200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1799999999999757 " " y[1] (analytic) = 13.80093845753068 " " y[1] (numeric) = 13.800938457530725 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 3.2178189274348873000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 644847683.0288188 " " Order of pole (six term test) = 24785312074865.875 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1899999999999755 " " y[1] (analytic) = 13.820083888227666 " " y[1] (numeric) = 13.82008388822771 " " absolute error = 4.44089209850062600000000000000E-14 " " relative error = 3.2133611737939610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 91.58934435839139 " " Order of pole (six term test) = -198282496599033.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999753 " " y[1] (analytic) = 13.83925587853273 " " y[1] (numeric) = 13.839255878532777 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 3.3372659794554780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.209999999999975 " " y[1] (analytic) = 13.858454465290844 " " y[1] (numeric) = 13.858454465290892 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 3.46082131913980350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.219999999999975 " " y[1] (analytic) = 13.877679685398089 " " y[1] (numeric) = 13.877679685398137 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 3.45602692604811750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2299999999999747 " " y[1] (analytic) = 13.89693157580173 " " y[1] (numeric) = 13.896931575801776 " " absolute error = 4.61852778244065100000000000000E-14 " " relative error = 3.3234155016512723000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2399999999999745 " " y[1] (analytic) = 13.916210173500284 " " y[1] (numeric) = 13.916210173500332 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 3.446458056169410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013469 " " Order of pole (six term test) = -396564993198057.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999742 " " y[1] (analytic) = 13.935515515543603 " " y[1] (numeric) = 13.935515515543651 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 3.4416835609928170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.259999999999974 " " y[1] (analytic) = 13.954847639032932 " " y[1] (numeric) = 13.95484763903298 " " absolute error = 4.79616346638067600000000000000E-14 " " relative error = 3.4369156800862420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 631819114.0946347 " " Order of pole (six term test) = 79312998639596.69 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.269999999999974 " " y[1] (analytic) = 13.974206581120983 " " y[1] (numeric) = 13.974206581121033 " " absolute error = 4.97379915032070130000000000000E-14 " " relative error = 3.55927123407511040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996492 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.2799999999999736 " " y[1] (analytic) = 13.99359237901201 " " y[1] (numeric) = 13.993592379012062 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 3.68128118551387550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2899999999999734 " " y[1] (analytic) = 14.013005069961881 " " y[1] (numeric) = 14.013005069961935 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.802946257133729700000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -14. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.299999999999973 " " y[1] (analytic) = 14.032444691278146 " " y[1] (numeric) = 14.032444691278199 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.7976779067677574000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.309999999999973 " " y[1] (analytic) = 14.051911280320109 " " y[1] (numeric) = 14.05191128032016 " " absolute error = 5.151434834260726000000000000000E-14 " " relative error = 3.66600295966526660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3199999999999728 " " y[1] (analytic) = 14.071404874498898 " " y[1] (numeric) = 14.07140487449895 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.7871630911981180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3299999999999725 " " y[1] (analytic) = 14.090925511277547 " " y[1] (numeric) = 14.0909255112776 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.78191660578694900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999723 " " y[1] (analytic) = 14.110473228171054 " " y[1] (numeric) = 14.11047322817111 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.9025666347935340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013458 " " Order of pole (six term test) = -594847489797080. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.349999999999972 " " y[1] (analytic) = 14.130048062746468 " " y[1] (numeric) = 14.130048062746523 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.8971602769413610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.359999999999972 " " y[1] (analytic) = 14.149650052622944 " " y[1] (numeric) = 14.149650052622999 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.89176140869999100000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -33047082766515.836 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3699999999999717 " " y[1] (analytic) = 14.16927923547183 " " y[1] (numeric) = 14.169279235471885 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.8863700196938110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -693988738096594.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3799999999999715 " " y[1] (analytic) = 14.188935649016733 " " y[1] (numeric) = 14.188935649016788 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.88098609956158400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643404 " " Order of pole (six term test) = -396564993198060. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999713 " " y[1] (analytic) = 14.208619331033587 " " y[1] (numeric) = 14.208619331033644 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 4.00062930369695650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013458 " " Order of pole (six term test) = -396564993198058. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.399999999999971 " " y[1] (analytic) = 14.228330319350741 " " y[1] (numeric) = 14.228330319350798 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.9950870963053280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.409999999999971 " " y[1] (analytic) = 14.248068651849014 " " y[1] (numeric) = 14.24806865184907 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.98955256672147430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4199999999999706 " " y[1] (analytic) = 14.267834366461779 " " y[1] (numeric) = 14.267834366461834 " " absolute error = 5.506706202140776000000000000000E-14 " " relative error = 3.859524901049410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013515 " " Order of pole (six term test) = -594847489797087. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4299999999999704 " " y[1] (analytic) = 14.287627501175029 " " y[1] (numeric) = 14.287627501175082 " " absolute error = 5.329070518200751000000000000000E-14 " " relative error = 3.7298498422936094000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.43999999999997 " " y[1] (analytic) = 14.307448094027452 " " y[1] (numeric) = 14.307448094027508 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.97299493852694250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013492 " " Order of pole (six term test) = -396564993198059. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.44999999999997 " " y[1] (analytic) = 14.327296183110512 " " y[1] (numeric) = 14.32729618311057 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.09147510814435340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013458 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4599999999999698 " " y[1] (analytic) = 14.347171806568515 " " y[1] (numeric) = 14.347171806568571 " " absolute error = 5.68434188608080100000000000000E-14 " " relative error = 3.9619947141626610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 52.8791326202186 " " Order of pole (six term test) = -198282496599033.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4699999999999696 " " y[1] (analytic) = 14.367075002598673 " " y[1] (numeric) = 14.367075002598732 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.08014684197063770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4799999999999693 " " y[1] (analytic) = 14.3870058094512 " " y[1] (numeric) = 14.387005809451258 " " absolute error = 5.86197757002082700000000000000E-14 " " relative error = 4.07449447623767560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.489999999999969 " " y[1] (analytic) = 14.406964265429362 " " y[1] (numeric) = 14.406964265429423 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 4.19214842397671200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.499999999999969 " " y[1] (analytic) = 14.426950408889573 " " y[1] (numeric) = 14.426950408889633 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 4.1863408986554590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5099999999999687 " " y[1] (analytic) = 14.446964278241444 " " y[1] (numeric) = 14.446964278241506 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 4.30349851924578250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542708 " " Order of pole (six term test) = -396564993198060. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5199999999999685 " " y[1] (analytic) = 14.467005911947881 " " y[1] (numeric) = 14.467005911947941 " " absolute error = 6.03961325396085200000000000000E-14 " " relative error = 4.17474997295253060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542684 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999683 " " y[1] (analytic) = 14.48707534852514 " " y[1] (numeric) = 14.487075348525202 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 4.291583213539250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.539999999999968 " " y[1] (analytic) = 14.507172626542914 " " y[1] (numeric) = 14.507172626542978 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 4.40808473605708700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.549999999999968 " " y[1] (analytic) = 14.5272977846244 " " y[1] (numeric) = 14.527297784624466 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.52425523536609860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562802 " " Order of pole (six term test) = -66094165533020.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5599999999999676 " " y[1] (analytic) = 14.547450861446377 " " y[1] (numeric) = 14.547450861446443 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.5179876312209490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5699999999999674 " " y[1] (analytic) = 14.567631895739279 " " y[1] (numeric) = 14.567631895739343 " " absolute error = 6.39488462184090200000000000000E-14 " " relative error = 4.38979009602190000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.579999999999967 " " y[1] (analytic) = 14.587840926287264 " " y[1] (numeric) = 14.587840926287326 " " absolute error = 6.21724893790087700000000000000E-14 " " relative error = 4.2619390829093870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.589999999999967 " " y[1] (analytic) = 14.60807799192829 " " y[1] (numeric) = 14.608077991928358 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 4.6208378634415550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996482 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.599999999999967 " " y[1] (analytic) = 14.628343131554214 " " y[1] (numeric) = 14.628343131554281 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 4.614436460107680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542715 " " Order of pole (six term test) = 49570624149744.375 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6099999999999666 " " y[1] (analytic) = 14.648636384110823 " " y[1] (numeric) = 14.64863638411089 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 4.6080439248548455000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6199999999999664 " " y[1] (analytic) = 14.668957788597945 " " y[1] (numeric) = 14.66895778859801 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.4805639231504846000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643165 " " Order of pole (six term test) = -264376662132043.34 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.629999999999966 " " y[1] (analytic) = 14.689307384069503 " " y[1] (numeric) = 14.689307384069568 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.47435684606123760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085394 " " Order of pole (six term test) = 198282496599010.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.639999999999966 " " y[1] (analytic) = 14.709685209633598 " " y[1] (numeric) = 14.709685209633667 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 4.7096804417839350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6499999999999657 " " y[1] (analytic) = 14.730091304452598 " " y[1] (numeric) = 14.730091304452664 " " absolute error = 6.57252030578092700000000000000E-14 " " relative error = 4.4619684765933470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.8664326 " " Order of pole (six term test) = -22031388511014.277 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6599999999999655 " " y[1] (analytic) = 14.750525707743178 " " y[1] (numeric) = 14.750525707743245 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 4.5762138404175710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999653 " " y[1] (analytic) = 14.77098845877643 " " y[1] (numeric) = 14.770988458776499 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 4.6901341051043290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = 33047082766491.67 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.679999999999965 " " y[1] (analytic) = 14.791479596877926 " " y[1] (numeric) = 14.791479596877993 " " absolute error = 6.75015598972095200000000000000E-14 " " relative error = 4.5635434545342735000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.689999999999965 " " y[1] (analytic) = 14.811999161427778 " " y[1] (numeric) = 14.81199916142785 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 4.9170020617520670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996492 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6999999999999647 " " y[1] (analytic) = 14.832547191860753 " " y[1] (numeric) = 14.832547191860824 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 4.7904296313313266000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7099999999999644 " " y[1] (analytic) = 14.8531237276663 " " y[1] (numeric) = 14.853123727666372 " " absolute error = 7.10542735760100200000000000000E-14 " " relative error = 4.7837932867724087000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999642 " " y[1] (analytic) = 14.873728808388666 " " y[1] (numeric) = 14.873728808388735 " " absolute error = 6.92779167366097700000000000000E-14 " " relative error = 4.6577369823724070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996482 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.729999999999964 " " y[1] (analytic) = 14.89436247362694 " " y[1] (numeric) = 14.894362473627014 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 5.0090755738565630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.90135 " " Order of pole (six term test) = -594847489797084. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.739999999999964 " " y[1] (analytic) = 14.915024763035165 " " y[1] (numeric) = 14.91502476303524 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 5.0021363316615920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7499999999999636 " " y[1] (analytic) = 14.935715716322383 " " y[1] (numeric) = 14.935715716322456 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 4.8762732097142070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.2996492 " " Order of pole (six term test) = 49570624149743.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7599999999999634 " " y[1] (analytic) = 14.95643537325272 " " y[1] (numeric) = 14.956435373252793 " " absolute error = 7.28306304154102700000000000000E-14 " " relative error = 4.8695179431361450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.256279 " " Order of pole (six term test) = -33047082766515.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.769999999999963 " " y[1] (analytic) = 14.97718377364547 " " y[1] (numeric) = 14.977183773645544 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 4.9813762308300140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.779999999999963 " " y[1] (analytic) = 14.997960957375167 " " y[1] (numeric) = 14.997960957375241 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 4.9744753614739160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.442209 " " Order of pole (six term test) = 24785312074866.125 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7899999999999627 " " y[1] (analytic) = 15.018766964371656 " " y[1] (numeric) = 15.018766964371732 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 5.0858598628909770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7999999999999625 " " y[1] (analytic) = 15.039601834620184 " " y[1] (numeric) = 15.039601834620258 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 4.9607022895426720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999623 " " y[1] (analytic) = 15.060465608161456 " " y[1] (numeric) = 15.060465608161532 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 5.0717783952720340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 533984612.4958798 " " Order of pole (six term test) = -56652141885447.07 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.819999999999962 " " y[1] (analytic) = 15.081358325091736 " " y[1] (numeric) = 15.081358325091811 " " absolute error = 7.46069872548105200000000000000E-14 " " relative error = 4.9469673517857154000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.829999999999962 " " y[1] (analytic) = 15.102280025562901 " " y[1] (numeric) = 15.102280025562978 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 5.0577359156975220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8399999999999617 " " y[1] (analytic) = 15.123230749782532 " " y[1] (numeric) = 15.123230749782614 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.4031057228685420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8499999999999615 " " y[1] (analytic) = 15.144210538013999 " " y[1] (numeric) = 15.14421053801408 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.3956206173509280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999612 " " y[1] (analytic) = 15.165219430576514 " " y[1] (numeric) = 15.165219430576593 " " absolute error = 7.99360577730112700000000000000E-14 " " relative error = 5.2710122750905990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 491870513.22374105 " " Order of pole (six term test) = 18025681508990.437 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.869999999999961 " " y[1] (analytic) = 15.186257467845222 " " y[1] (numeric) = 15.186257467845302 " " absolute error = 7.99360577730112700000000000000E-14 " " relative error = 5.2637101631040240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542701 " " Order of pole (six term test) = -99141248299523. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.879999999999961 " " y[1] (analytic) = 15.207324690251285 " " y[1] (numeric) = 15.207324690251367 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.3732274595802900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542708 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8899999999999606 " " y[1] (analytic) = 15.228421138281956 " " y[1] (numeric) = 15.228421138282037 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.365783745433650000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8999999999999604 " " y[1] (analytic) = 15.249546852480643 " " y[1] (numeric) = 15.249546852480726 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 5.4748362203451740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901351 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.90999999999996 " " y[1] (analytic) = 15.270701873447011 " " y[1] (numeric) = 15.270701873447093 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.3509272389433940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.91999999999996 " " y[1] (analytic) = 15.291886241837037 " " y[1] (numeric) = 15.291886241837119 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.3435144180483570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 549927951.8479991 " " Order of pole (six term test) = 36051363017992.22 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9299999999999597 " " y[1] (analytic) = 15.3130999983631 " " y[1] (numeric) = 15.313099998363185 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.5681167301412830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 706395244.299647 " " Order of pole (six term test) = -247853120748788.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9399999999999595 " " y[1] (analytic) = 15.334343183794067 " " y[1] (numeric) = 15.334343183794152 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.560403029281590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999593 " " y[1] (analytic) = 15.355615838955352 " " y[1] (numeric) = 15.355615838955433 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 5.3213375138701340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643106 " " Order of pole (six term test) = -22031388511014.14 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.959999999999959 " " y[1] (analytic) = 15.376918004729 " " y[1] (numeric) = 15.376918004729083 " " absolute error = 8.34887714518117700000000000000E-14 " " relative error = 5.4294866777683100000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.969999999999959 " " y[1] (analytic) = 15.39824972205378 " " y[1] (numeric) = 15.398249722053865 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.5373259838157480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085406 " " Order of pole (six term test) = -198282496599035.12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9799999999999587 " " y[1] (analytic) = 15.419611031925255 " " y[1] (numeric) = 15.41961103192534 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.5296549384207140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1412790488.5992997 " " Order of pole (six term test) = -495706241497570. " " " " "TOP MAIN SOLVE Loop" x[1] = 3.9899999999999585 " " y[1] (analytic) = 15.441001975395848 " " y[1] (numeric) = 15.441001975395935 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 5.6370360724845950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999583 " " y[1] (analytic) = 15.462422593574944 " " y[1] (numeric) = 15.462422593575031 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 5.6292268953236580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 64.76344648024842 " " Order of pole (six term test) = -198282496599033.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999958 " " y[1] (analytic) = 15.483872927628951 " " y[1] (numeric) = 15.483872927629037 " " absolute error = 8.52651282912120200000000000000E-14 " " relative error = 5.506705505123820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999958 " " y[1] (analytic) = 15.50535301878138 " " y[1] (numeric) = 15.505353018781468 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 5.7282050826207520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.029999999999958 " " y[1] (analytic) = 15.526862908312944 " " y[1] (numeric) = 15.526862908313031 " " absolute error = 8.70414851306122700000000000000E-14 " " relative error = 5.6058642138207480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 491870513.22373986 " " Order of pole (six term test) = -162231133581030.34 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999957 " " y[1] (analytic) = 15.548402637561606 " " y[1] (numeric) = 15.548402637561697 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 5.8265920249940420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999957 " " y[1] (analytic) = 15.569972247922694 " " y[1] (numeric) = 15.569972247922783 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 5.7044316172022970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999957 " " y[1] (analytic) = 15.591571780848945 " " y[1] (numeric) = 15.591571780849034 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 5.6965290747086230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1289695366.0576377 " " Order of pole (six term test) = -594847489797083.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999957 " " y[1] (analytic) = 15.613201277850608 " " y[1] (numeric) = 15.613201277850699 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 5.8024102294724540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0799999999999566 " " y[1] (analytic) = 15.634860780495522 " " y[1] (numeric) = 15.634860780495613 " " absolute error = 9.05941988094127700000000000000E-14 " " relative error = 5.794371953885830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = 33047082766492.33 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999956 " " y[1] (analytic) = 15.656550330409182 " " y[1] (numeric) = 15.656550330409276 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 6.0132602968966250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085409 " " Order of pole (six term test) = -991412482995130.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999956 " " y[1] (analytic) = 15.678269969274837 " " y[1] (numeric) = 15.678269969274933 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 6.1182304881595450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999956 " " y[1] (analytic) = 15.700019738833559 " " y[1] (numeric) = 15.700019738833653 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 5.9966110905799390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1053031856.8243899 " " Order of pole (six term test) = -264376662132041.84 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999956 " " y[1] (analytic) = 15.721799680884322 " " y[1] (numeric) = 15.721799680884414 " " absolute error = 9.23705556488130200000000000000E-14 " " relative error = 5.8753169181466990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.42305267 " " Order of pole (six term test) = -89227123469571.9 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.1299999999999555 " " y[1] (analytic) = 15.743609837284087 " " y[1] (numeric) = 15.743609837284179 " " absolute error = 9.23705556488130200000000000000E-14 " " relative error = 5.8671776424527920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999955 " " y[1] (analytic) = 15.765450249947879 " " y[1] (numeric) = 15.765450249947975 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 6.0843977055416250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999955 " " y[1] (analytic) = 15.78732096084888 " " y[1] (numeric) = 15.787320960848975 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 5.9634508427167000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542688 " " Order of pole (six term test) = -11.703125 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999955 " " y[1] (analytic) = 15.80922201201849 " " y[1] (numeric) = 15.809222012018584 " " absolute error = 9.41469124882132700000000000000E-14 " " relative error = 5.9551894721094370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.169999999999955 " " y[1] (analytic) = 15.831153445546414 " " y[1] (numeric) = 15.831153445546512 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 6.1713523593253040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999954 " " y[1] (analytic) = 15.853115303580763 " " y[1] (numeric) = 15.853115303580859 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 6.0507520125049000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 549927951.8479974 " " Order of pole (six term test) = -54077044527017.87 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999954 " " y[1] (analytic) = 15.875107628328099 " " y[1] (numeric) = 15.875107628328196 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 6.154265435824520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999954 " " y[1] (analytic) = 15.89713046205355 " " y[1] (numeric) = 15.897130462053646 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 6.0339990010513130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.9013469 " " Order of pole (six term test) = -396564993198056.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999954 " " y[1] (analytic) = 15.919183847080863 " " y[1] (numeric) = 15.91918384708096 " " absolute error = 9.76996261670137800000000000000E-14 " " relative error = 6.1372258217200740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.219999999999954 " " y[1] (analytic) = 15.941267825792506 " " y[1] (numeric) = 15.941267825792607 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 6.3515863952797370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 91.58934435839139 " " Order of pole (six term test) = -198282496599033.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999953 " " y[1] (analytic) = 15.963382440629752 " " y[1] (numeric) = 15.963382440629852 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.2315103566791270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999953 " " y[1] (analytic) = 15.985527734092733 " " y[1] (numeric) = 15.985527734092832 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.2228776341402300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 762994068.1490815 " " Order of pole (six term test) = -223067808673911.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999953 " " y[1] (analytic) = 16.007703748740546 " " y[1] (numeric) = 16.00770374874065 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.4361946161903840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999953 " " y[1] (analytic) = 16.02991052719134 " " y[1] (numeric) = 16.02991052719144 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.2056480501044690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 543783312.6008978 " " Order of pole (six term test) = 66094165532995.81 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.2699999999999525 " " y[1] (analytic) = 16.052148112122367 " " y[1] (numeric) = 16.052148112122467 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.1970511554955750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999952 " " y[1] (analytic) = 16.074416546270097 " " y[1] (numeric) = 16.074416546270196 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.1884661704562090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999952 " " y[1] (analytic) = 16.09671587243028 " " y[1] (numeric) = 16.09671587243038 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.179893078487640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999952 " " y[1] (analytic) = 16.119046133458035 " " y[1] (numeric) = 16.119046133458138 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3917365725109240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901351 " " Order of pole (six term test) = -11.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.309999999999952 " " y[1] (analytic) = 16.14140737226794 " " y[1] (numeric) = 16.14140737226804 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3828818831637320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 499496867.44220865 " " Order of pole (six term test) = -86748592262084.62 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999951 " " y[1] (analytic) = 16.163799631834095 " " y[1] (numeric) = 16.1637996318342 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3740394605178570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999951 " " y[1] (analytic) = 16.186222955190228 " " y[1] (numeric) = 16.186222955190328 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.1457193121460340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -495706241497570. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999951 " " y[1] (analytic) = 16.208677385429745 " " y[1] (numeric) = 16.208677385429848 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3563913473796920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 446763580.05959237 " " Order of pole (six term test) = 99141248299499.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999950 " " y[1] (analytic) = 16.23116296570586 " " y[1] (numeric) = 16.231162965705963 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3475856229710410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901351 " " Order of pole (six term test) = -11.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.359999999999950 " " y[1] (analytic) = 16.253679739231636 " " y[1] (numeric) = 16.25367973923174 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3387920974309180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.36999999999995 " " y[1] (analytic) = 16.27622774928009 " " y[1] (numeric) = 16.27622774928019 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.1117345209681000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.37999999999995 " " y[1] (analytic) = 16.29880703918426 " " y[1] (numeric) = 16.29880703918436 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 6.103267727954690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 744605966.76599 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.38999999999995 " " y[1] (analytic) = 16.321417652337306 " " y[1] (numeric) = 16.32141765233741 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3124845451436830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.39999999999995 " " y[1] (analytic) = 16.344059632192586 " " y[1] (numeric) = 16.34405963219269 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.3037396463165640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901349 " " Order of pole (six term test) = -297423744898546.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4099999999999495 " " y[1] (analytic) = 16.366733022263737 " " y[1] (numeric) = 16.36673302226384 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.2950068620942330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562807 " " Order of pole (six term test) = -33047082766515.164 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.419999999999950 " " y[1] (analytic) = 16.38943786612476 " " y[1] (numeric) = 16.38943786612486 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.286286175693919000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 425972359.8242487 " " Order of pole (six term test) = 18025681508991.625 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.429999999999949 " " y[1] (analytic) = 16.412174207410104 " " y[1] (numeric) = 16.412174207410207 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 6.2775775703560970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.439999999999949 " " y[1] (analytic) = 16.434942089814747 " " y[1] (numeric) = 16.434942089814854 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4850493407011690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 421212742.7297542 " " Order of pole (six term test) = 13218833106590.281 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.449999999999949 " " y[1] (analytic) = 16.457741557094295 " " y[1] (numeric) = 16.4577415570944 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4760653820129970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1153538603.5085402 " " Order of pole (six term test) = -693988738096594.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.4599999999999485 " " y[1] (analytic) = 16.480572653065042 " " y[1] (numeric) = 16.48057265306515 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.467093869107340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999948 " " y[1] (analytic) = 16.50343542160407 " " y[1] (numeric) = 16.503435421604177 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4581347847426380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999948 " " y[1] (analytic) = 16.52632990664933 " " y[1] (numeric) = 16.526329906649437 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.449188111701211000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999948 " " y[1] (analytic) = 16.549256152199728 " " y[1] (numeric) = 16.549256152199835 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4402538327892290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.499999999999948 " " y[1] (analytic) = 16.572214202315205 " " y[1] (numeric) = 16.572214202315312 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4313319308366880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999947 " " y[1] (analytic) = 16.595204101116824 " " y[1] (numeric) = 16.595204101116934 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 6.6365031349872780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999947 " " y[1] (analytic) = 16.618225892786864 " " y[1] (numeric) = 16.61822589278697 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4135251892487910000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 689371170.4425216 " " Order of pole (six term test) = -84978212828163.64 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999947 " " y[1] (analytic) = 16.64127962156888 " " y[1] (numeric) = 16.641279621568987 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 6.4046403153922190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999947 " " y[1] (analytic) = 16.66436533176781 " " y[1] (numeric) = 16.664365331767925 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.8221522667227640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542694 " " Order of pole (six term test) = 99141248299500.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.5499999999999465 " " y[1] (analytic) = 16.687483067750073 " " y[1] (numeric) = 16.687483067750186 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.8127013079237310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 407837484.45067084 " " Order of pole (six term test) = -132188331066026.67 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999946 " " y[1] (analytic) = 16.710632873943606 " " y[1] (numeric) = 16.71063287394372 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.80326344185829900000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.754267 " " Order of pole (six term test) = -198282496599034.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999946 " " y[1] (analytic) = 16.733814794838 " " y[1] (numeric) = 16.73381479483811 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 6.5815311925640160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999946 " " y[1] (analytic) = 16.757028874984552 " " y[1] (numeric) = 16.757028874984663 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 6.5724135742958220000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542701 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999946 " " y[1] (analytic) = 16.780275158996368 " " y[1] (numeric) = 16.78027515899648 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7750282188111430000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.5999999999999455 " " y[1] (analytic) = 16.80355369154845 " " y[1] (numeric) = 16.803553691548565 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7656425425531370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999945 " " y[1] (analytic) = 16.82686451737777 " " y[1] (numeric) = 16.82686451737788 " " absolute error = 1.10134124042815530000000000000E-13 " " relative error = 6.545136435197160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999945 " " y[1] (analytic) = 16.85020768128335 " " y[1] (numeric) = 16.850207681283464 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7469101789110630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999945 " " y[1] (analytic) = 16.873583228126385 " " y[1] (numeric) = 16.8735832281265 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7375634555269050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.639999999999945 " " y[1] (analytic) = 16.89699120283028 " " y[1] (numeric) = 16.896991202830396 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 6.9384868579903550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999944 " " y[1] (analytic) = 16.920431650380777 " " y[1] (numeric) = 16.92043165038089 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7189088358190690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 665995823.2562823 " " Order of pole (six term test) = -99141248299524. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999944 " " y[1] (analytic) = 16.943904615826014 " " y[1] (numeric) = 16.943904615826128 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7096009036447110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999944 " " y[1] (analytic) = 16.967410144276627 " " y[1] (numeric) = 16.96741014427674 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.7003058660643260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 257939073.2115244 " " Order of pole (six term test) = 118969497959402.4 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999944 " " y[1] (analytic) = 16.99094828090583 " " y[1] (numeric) = 16.990948280905943 " " absolute error = 1.13686837721616030000000000000E-13 " " relative error = 6.6910237052145920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.90135 " " Order of pole (six term test) = -198282496599036. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.6899999999999435 " " y[1] (analytic) = 17.014519070949504 " " y[1] (numeric) = 17.01451907094962 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 6.8905592283587190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542683 " " Order of pole (six term test) = -11.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999943 " " y[1] (analytic) = 17.038122559706284 " " y[1] (numeric) = 17.038122559706405 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0895290637761050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999943 " " y[1] (analytic) = 17.061758792537656 " " y[1] (numeric) = 17.061758792537777 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0797076988363140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901349 " " Order of pole (six term test) = -198282496599035.75 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999943 " " y[1] (analytic) = 17.08542781486802 " " y[1] (numeric) = 17.085427814868137 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 6.8619617062437710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999943 " " y[1] (analytic) = 17.10912967218479 " " y[1] (numeric) = 17.109129672184906 " " absolute error = 1.17239551400416530000000000000E-13 " " relative error = 6.852455598078669000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7399999999999425 " " y[1] (analytic) = 17.132864410038486 " " y[1] (numeric) = 17.132864410038607 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0503251638670780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999942 " " y[1] (analytic) = 17.156632074042832 " " y[1] (numeric) = 17.156632074042953 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0405581094188040000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643404 " " Order of pole (six term test) = -231329579365540. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999942 " " y[1] (analytic) = 17.180432709874815 " " y[1] (numeric) = 17.180432709874935 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0308045856021510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999942 " " y[1] (analytic) = 17.204266363274787 " " y[1] (numeric) = 17.204266363274908 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0210645736726750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1823904678.008439 " " Order of pole (six term test) = -1586259972792192.5 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.779999999999942 " " y[1] (analytic) = 17.22813308004656 " " y[1] (numeric) = 17.228133080046682 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 7.0113380549119010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999941 " " y[1] (analytic) = 17.25203290605748 " " y[1] (numeric) = 17.252032906057607 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.413485305370070000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 815674968.901351 " " Order of pole (six term test) = -198282496599036.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999941 " " y[1] (analytic) = 17.27596588723854 " " y[1] (numeric) = 17.275965887238666 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1975702875095990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.4230537 " " Order of pole (six term test) = -39656499319816.305 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999941 " " y[1] (analytic) = 17.299932069584433 " " y[1] (numeric) = 17.299932069584557 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1875992494000850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -99141248299525. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999940 " " y[1] (analytic) = 17.323931499153666 " " y[1] (numeric) = 17.323931499153787 " " absolute error = 1.20792265079217030000000000000E-13 " " relative error = 6.9725665380931670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 911952339.0042195 " " Order of pole (six term test) = -346994369048301.25 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.829999999999940 " " y[1] (analytic) = 17.347964222068633 " " y[1] (numeric) = 17.347964222068757 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1676985936964420000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.83999999999994 " " y[1] (analytic) = 17.37203028451572 " " y[1] (numeric) = 17.372030284515848 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.362276621795760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.84999999999994 " " y[1] (analytic) = 17.39612973274539 " " y[1] (numeric) = 17.396129732745518 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.3520774104179840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.85999999999994 " " y[1] (analytic) = 17.42026261307226 " " y[1] (numeric) = 17.420262613072385 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1379508747880980000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.86999999999994 " " y[1] (analytic) = 17.444428971875194 " " y[1] (numeric) = 17.44442897187532 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1280624294720630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 689371170.4425275 " " Order of pole (six term test) = -254934638484472. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.8799999999999395 " " y[1] (analytic) = 17.468628855597398 " " y[1] (numeric) = 17.468628855597522 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.1181876829545320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.889999999999940 " " y[1] (analytic) = 17.492862310746506 " " y[1] (numeric) = 17.492862310746634 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.3114216624369010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.899999999999939 " " y[1] (analytic) = 17.517129383894677 " " y[1] (numeric) = 17.517129383894805 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.3012929021582560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 644847683.0288188 " " Order of pole (six term test) = 24785312074865.875 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.909999999999939 " " y[1] (analytic) = 17.54143012167867 " " y[1] (numeric) = 17.541430121678797 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.2911781735945800000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.919999999999939 " " y[1] (analytic) = 17.565764570799942 " " y[1] (numeric) = 17.56576457080007 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.2810774573072620000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999938 " " y[1] (analytic) = 17.590132778024746 " " y[1] (numeric) = 17.59013277802487 " " absolute error = 1.24344978758017530000000000000E-13 " " relative error = 7.069018769054490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999938 " " y[1] (analytic) = 17.614534790184187 " " y[1] (numeric) = 17.61453479018432 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 7.4626101501624730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 470930162.86643404 " " Order of pole (six term test) = -462659158731068. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999938 " " y[1] (analytic) = 17.638970654174372 " " y[1] (numeric) = 17.638970654174503 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 7.4522719433466480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.423054 " " Order of pole (six term test) = -49570624149768. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999938 " " y[1] (analytic) = 17.663440416956437 " " y[1] (numeric) = 17.66344041695657 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 7.4419480583991780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 515878146.4230547 " " Order of pole (six term test) = -99141248299523. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.969999999999938 " " y[1] (analytic) = 17.68794412555668 " " y[1] (numeric) = 17.687944125556808 " " absolute error = 1.27897692436818030000000000000E-13 " " relative error = 7.2307833815476160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542704 " " Order of pole (six term test) = -99141248299523.94 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999937 " " y[1] (analytic) = 17.71248182706662 " " y[1] (numeric) = 17.712481827066753 " " absolute error = 1.31450406115618530000000000000E-13 " " relative error = 7.4213431747745160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445154 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999937 " " y[1] (analytic) = 17.737053568643127 " " y[1] (numeric) = 17.73705356864326 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 7.6113611131607300000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.05602888445156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 576769301.7542679 " " Order of pole (six term test) = -99141248299525. " " " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999937 " " y[1] (analytic) = 17.761659397508474 " " y[1] (numeric) = 17.76165939750861 " " absolute error = 1.35003119794419040000000000000E-13 " " relative error = 7.6008168365933570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 137.0560288844515 " " "Order 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 ) = expt(2.0 , (0.2 * x + 0.3));" Iterations = 401 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 1 Minutes 48 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 1 Minutes 45 Seconds "Time to Timeout "= 0 Years 0 Days 0 Hours 1 Minutes 11 Seconds Percent Done = 100.49999999999841 "%" (%o58) true (%o58) diffeq.max