(%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_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_const_0D2 array_x , 1 1 1 array_tmp2 1 array_tmp4 : array_const_0D3 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 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_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_0D2 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp2 - array_tmp5 array_tmp4 2 1 2 array_tmp5 : -------------------------------------, 2 array_tmp4 1 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 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_tmp5 array_tmp4 2 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 3 array_tmp4 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - array_tmp5 array_tmp4 3 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 4 array_tmp4 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - array_tmp5 array_tmp4 4 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 5 array_tmp4 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp5 : kkk - array_tmp5 array_tmp4 kkk - 1 2 -------------------------------, array_tmp6 : array_tmp5 , order_d : 1, array_tmp4 kkk kkk 1 if order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp6 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_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_const_0D2 array_x , 1 1 1 array_tmp2 1 array_tmp4 : array_const_0D3 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 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_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_0D2 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp2 - array_tmp5 array_tmp4 2 1 2 array_tmp5 : -------------------------------------, 2 array_tmp4 1 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 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_tmp5 array_tmp4 2 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 3 array_tmp4 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - array_tmp5 array_tmp4 3 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 4 array_tmp4 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - array_tmp5 array_tmp4 4 2 array_tmp5 : -------------------------, array_tmp6 : array_tmp5 , 5 array_tmp4 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp5 : kkk - array_tmp5 array_tmp4 kkk - 1 2 -------------------------------, array_tmp6 : array_tmp5 , order_d : 1, array_tmp4 kkk kkk 1 if order_d + kkk < glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp6 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(0.25 ln(3.0 + 2.0 x) + 0.5 x) (%o56) exact_soln_y(x) := block(0.25 ln(3.0 + 2.0 x) + 0.5 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/div_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) / (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:0.1,"), 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, " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) "), 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, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 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_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6 : 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, 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, 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 : 0.1, 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 ) = (0.1 * x + 0.2) / (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, "2013-05-26T00:41:03-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) / (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, "div_lin_lin diffeq.max"), logitem_str(html_log_file, "div_lin_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/div_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) / (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:0.1,"), 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, " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) "), 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, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 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 : 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_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6 : 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, 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_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 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_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, 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 : 0.1, 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 ) = (0.1 * x + 0.2) / (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, "2013-05-26T00:41:03-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) / (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, "div_lin_lin diffeq.max"), logitem_str(html_log_file, "div_lin_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/div_lin_linpostode.ode#################" "diff ( y , x , 1 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "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(" " (0.5 * x + 0.25 * ln(2.0 * x + 3.0)) " "));" "/* 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 = 4.9 "" estimated_steps = 4900000.000000001 "" step_error = 2.04081632653061200000000000000000E-17 "" est_needed_step_err = 2.04081632653061200000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 4.7407492057234600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-164 "" estimated_step_error = 4.7407492057234600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-164 "" 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 = 3.1814619796659344000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-156 "" estimated_step_error = 3.1814619796659344000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-156 "" 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 = 2.13504170816769060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-148 "" estimated_step_error = 2.13504170816769060000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-148 "" 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 = 1.432800511612334300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-140 "" estimated_step_error = 1.432800511612334300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-140 "" 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 = 9.615338319311519000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-133 "" estimated_step_error = 9.615338319311519000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-133 "" 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 = 6.45271324737752500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-125 "" estimated_step_error = 6.45271324737752500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-125 "" 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 = 4.330300858702338000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-117 "" estimated_step_error = 4.330300858702338000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-117 "" 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 = 2.9059597485076333000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-109 "" estimated_step_error = 2.9059597485076333000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-109 "" 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 = 1.950081464177621500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-101 "" estimated_step_error = 1.950081464177621500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-101 "" 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 = 1.3085767166128032000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" estimated_step_error = 1.3085767166128032000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-93 "" 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 = 8.78035707497457300000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" estimated_step_error = 8.78035707497457300000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-86 "" 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 = 5.890583278514203000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" estimated_step_error = 5.890583278514203000000000000000000000000000000000000000000000000000000000000000000000000000000E-78 "" 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 = 3.9506702500394020000000000000000000000000000000000000000000000000000000000000000000000E-70 "" estimated_step_error = 3.9506702500394020000000000000000000000000000000000000000000000000000000000000000000000E-70 "" 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 = 2.647990101701283600000000000000000000000000000000000000000000000000000000000000E-62 "" estimated_step_error = 2.647990101701283600000000000000000000000000000000000000000000000000000000000000E-62 "" 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 = 1.77267707624364000000000000000000000000000000000000000000000000000000E-54 "" estimated_step_error = 1.77267707624364000000000000000000000000000000000000000000000000000000E-54 "" 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 = 1.18381654847695140000000000000000000000000000000000000000000000E-46 "" estimated_step_error = 1.18381654847695140000000000000000000000000000000000000000000000E-46 "" 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 = 7.86769122722829100000000000000000000000000000000000000E-39 "" estimated_step_error = 7.86769122722829100000000000000000000000000000000000000E-39 "" 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 = 5.1800284532005440000000000000000000000000000000E-31 "" estimated_step_error = 5.1800284532005440000000000000000000000000000000E-31 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 0.3407877024514202 " " y[1] (numeric) = 0.3407877024514202 " " 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 = 1.6727272727272726 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11 " " y[1] (analytic) = 0.34734533988907923 " " y[1] (numeric) = 0.34734533988907923 " " 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 = 1.6831818181818186 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12 " " y[1] (analytic) = 0.35389333245105953 " " y[1] (numeric) = 0.3538933324510595 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.568584263704220800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.6936363636363634 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.081955575315096 " " Order of pole (six term test) = 9.17896869623291400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13 " " y[1] (analytic) = 0.36043179884465404 " " y[1] (numeric) = 0.36043179884465404 " " 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 = 1.7040909090909089 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.1782024173470735 " " Order of pole (six term test) = 8.98037200158796600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14 " " y[1] (analytic) = 0.3669608555990131 " " y[1] (numeric) = 0.36696085559901304 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.512726776828648700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7145454545454546 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000002 " " y[1] (analytic) = 0.37348061711810865 " " y[1] (numeric) = 0.3734806171181086 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.48631946845324800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7250000000000003 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9050201669894901 " " Order of pole (six term test) = -2.614797267597168700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000003 " " y[1] (analytic) = 0.37999119573209933 " " y[1] (numeric) = 0.3799911957320993 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.460853615945201800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7354545454545454 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4449388661475198 " " Order of pole (six term test) = 1.22728494034163300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000004 " " y[1] (analytic) = 0.3864927017471523 " " y[1] (numeric) = 0.3864927017471522 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.436279416928649400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7459090909090913 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1442960620976446 " " Order of pole (six term test) = 9.2370555648813020000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000005 " " y[1] (analytic) = 0.3929852434937783 " " y[1] (numeric) = 0.39298524349377817 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.82510105151755800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7563636363636361 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4145467866141415 " " Order of pole (six term test) = 2.6942004183183600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000006 " " y[1] (analytic) = 0.39946892737373185 " " y[1] (numeric) = 0.3994689273737318 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.38962375862899500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7668181818181818 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2789731342442296 " " Order of pole (six term test) = 2.246558494789496800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000007 " " y[1] (analytic) = 0.405943857905529 " " y[1] (numeric) = 0.4059438579055289 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.734917656725642000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7772727272727276 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.5098883540204606 " " Order of pole (six term test) = 2.94395618993803500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000008 " " y[1] (analytic) = 0.4124101377686285 " " y[1] (numeric) = 0.4124101377686284 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.692036210923643400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7877272727272728 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000008 " " y[1] (analytic) = 0.4188678678463268 " " y[1] (numeric) = 0.4188678678463267 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.650532804852131500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.7981818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 9.035826800743699 " " Order of pole (six term test) = 4.18058476725491350000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000001 " " y[1] (analytic) = 0.42531714726740827 " " y[1] (numeric) = 0.42531714726740816 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.610341557489873600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8086363636363638 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000001 " " y[1] (analytic) = 0.43175807344659584 " " y[1] (numeric) = 0.43175807344659567 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.85710109285013760000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.819090909090909 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 0.43819074212384207 " " y[1] (numeric) = 0.4381907421238419 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.800478597211156600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8295454545454548 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 0.4446152474025015 " " y[1] (numeric) = 0.44461524740250136 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.74556326321877130000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8400000000000003 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 0.45103168178642083 " " y[1] (numeric) = 0.4510316817864207 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.461518934164109700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8504545454545458 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 0.4574401362159849 " " y[1] (numeric) = 0.4574401362159847 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.64055185606063800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8609090909090913 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 0.4638407001031523 " " y[1] (numeric) = 0.4638407001031522 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.393543784273904600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8713636363636366 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 0.4702334613655162 " " y[1] (numeric) = 0.470233461365516 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.54150581309494950000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8818181818181818 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 0.47661850645942 " " y[1] (numeric) = 0.4766185064594199 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.329374561790505000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.8922727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.227180059386747 " " Order of pole (six term test) = 2.431477241771062800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 0.48299592041216244 " " y[1] (numeric) = 0.48299592041216227 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.44792671440501800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9027272727272733 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3543171584448965 " " Order of pole (six term test) = -4.309441692385007600000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 0.48936578685331883 " " y[1] (numeric) = 0.48936578685331866 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.4030465179146200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9131818181818185 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 0.49572818804521 " " y[1] (numeric) = 0.49572818804520985 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 3.359370270035678000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.923636363636364 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 0.5020832049125448 " " y[1] (numeric) = 0.5020832049125447 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.21123314574631220000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9340909090909097 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 0.508430917071264 " " y[1] (numeric) = 0.5084309170712638 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.36725221597624670000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9445454545454548 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.7633516246027074 " " Order of pole (six term test) = 1.82254211722465700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 0.5147714028566103 " " y[1] (numeric) = 0.51477140285661 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.313460376641821700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9550000000000005 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 0.5211047393504509 " " y[1] (numeric) = 0.5211047393504507 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.26103599061114900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9654545454545458 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 0.5274310024078742 " " y[1] (numeric) = 0.527431002407874 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.20992705986818800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9759090909090915 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 0.5337502666830851 " " y[1] (numeric) = 0.5337502666830849 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 4.16008419639573800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9863636363636368 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4402021076439133 " " Order of pole (six term test) = -1.9326762412674725000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 0.5400626056546212 " " y[1] (numeric) = 0.5400626056546208 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.16719069049095900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 1.9968181818181823 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 0.5463680916499091 " " y[1] (numeric) = 0.5463680916499087 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.09601681499663800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0072727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 0.5526667958691851 " " y[1] (numeric) = 0.5526667958691848 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 6.02654094432666300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.017727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.85597702368483 " " Order of pole (six term test) = 3.621281052801350600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 0.5589587884087956 " " y[1] (numeric) = 0.5589587884087954 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.97246826652698670000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0281818181818188 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.8334139243670947 " " Order of pole (six term test) = -1.788791337276052200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 0.5652441382839004 " " y[1] (numeric) = 0.5652441382839001 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.89244336790026500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0386363636363636 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 0.571522913450593 " " y[1] (numeric) = 0.5715229134505927 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.82770873308721500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0490909090909093 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.00583072533312 " " Order of pole (six term test) = 1.188560361242707600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 0.5777951808274608 " " y[1] (numeric) = 0.5777951808274605 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.76444592200581500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.059545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5611006830578738 " " Order of pole (six term test) = 1.97086791331457800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.5840610063165975 " " y[1] (numeric) = 0.5840610063165972 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.70260475850024300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0700000000000003 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.8952357050820803 " " Order of pole (six term test) = 5.13651343680976400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.5903204548240868 " " y[1] (numeric) = 0.5903204548240865 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.642137328390554000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0804545454545456 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 0.5965735902799729 " " y[1] (numeric) = 0.5965735902799725 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.44399713774877100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.0909090909090917 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.00299220175089 " " Order of pole (six term test) = -9.63069624049239800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 0.6028204756577327 " " y[1] (numeric) = 0.6028204756577322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.36685676387352800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1013636363636365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 0.6090611729932649 " " y[1] (numeric) = 0.6090611729932645 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.29137284630313200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1118181818181827 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.644292353051684 " " Order of pole (six term test) = 4.881783866039768300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 0.6152957434034105 " " y[1] (numeric) = 0.6152957434034101 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.21749198838356800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.122272727272728 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 0.6215242471040179 " " y[1] (numeric) = 0.6215242471040173 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.93145383947788500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1327272727272732 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 0.6277467434275658 " " y[1] (numeric) = 0.6277467434275653 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.0743371351524200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.143181818181818 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 0.633963290840359 " " y[1] (numeric) = 0.6339632908403585 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 7.00496726334728100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1536363636363647 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 0.640173946959306 " " y[1] (numeric) = 0.6401739469593055 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.93700847963892800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.16409090909091 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 16.758541561318026 " " Order of pole (six term test) = -6.2875038508991570000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 0.6463787685682932 " " y[1] (numeric) = 0.6463787685682928 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.87041764743766100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.1745454545454557 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 0.6525778116341665 " " y[1] (numeric) = 0.6525778116341661 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.80515337685152400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.185 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 0.658771131322331 " " y[1] (numeric) = 0.6587711313223304 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.42646992132639400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.195454545454546 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 0.6649587820119804 " " y[1] (numeric) = 0.6649587820119799 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.34805896739892800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2059090909090915 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 0.6711408173109669 " " y[1] (numeric) = 0.6711408173109664 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.61693043241472200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2163636363636376 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6834254695262922 " " Order of pole (six term test) = 1.07114317415835100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 0.67731729007032 " " y[1] (numeric) = 0.6773172900703196 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.5565904836706100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2268181818181825 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 0.6834882523984267 " " y[1] (numeric) = 0.6834882523984261 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 8.12174182020887800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.237272727272728 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 0.6896537556748794 " " y[1] (numeric) = 0.689653755674879 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 6.43930677090980300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.247727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 0.695813850564005 " " y[1] (numeric) = 0.6958138505640045 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.97787385034980500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2581818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.6968481202477874 " " Order of pole (six term test) = 4.81428230614255900000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 0.7019685870280787 " " y[1] (numeric) = 0.7019685870280781 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.48951031548721700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.268636363636364 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6800000000000005 " " y[1] (analytic) = 0.7081180143402361 " " y[1] (numeric) = 0.7081180143402355 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.40710165939981800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2790909090909093 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000005 " " y[1] (analytic) = 0.714262181097089 " " y[1] (numeric) = 0.7142621810970884 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.32618067152777000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.2895454545454554 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 0.7204011352310542 " " y[1] (numeric) = 0.7204011352310535 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.2467068997808410000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3000000000000003 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.219079097579113 " " Order of pole (six term test) = 4.023448241241567300000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 0.7265349240224019 " " y[1] (numeric) = 0.7265349240224014 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 7.64053445964095200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3104545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 0.7326635941110337 " " y[1] (numeric) = 0.732663594111033 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 9.09194642847427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3209090909090913 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 0.7387871915079935 " " y[1] (numeric) = 0.7387871915079928 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.05193501751336320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3313636363636365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 0.7449057616067238 " " y[1] (numeric) = 0.7449057616067231 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.04329454448214130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3418181818181822 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 0.7510193491940689 " " y[1] (numeric) = 0.7510193491940681 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.03480172391242450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.352272727272728 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 0.7571279984610353 " " y[1] (numeric) = 0.7571279984610345 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.02645275147304580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.3627272727272732 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000006 " " y[1] (analytic) = 0.7632317530133145 " " y[1] (numeric) = 0.7632317530133137 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.01824395299241730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.373181818181819 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000006 " " y[1] (analytic) = 0.769330655881574 " " y[1] (numeric) = 0.7693306558815732 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.01017177893043710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.383636363636364 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9579271068850972 " " Order of pole (six term test) = -1.5134560271690134000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000006 " " y[1] (analytic) = 0.7754247495315237 " " y[1] (numeric) = 0.775424749531523 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 1.00223279912993730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.39409090909091 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 0.7815140758737626 " " y[1] (numeric) = 0.7815140758737619 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.94423697831314600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.404545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000006 " " y[1] (analytic) = 0.7875986762734122 " " y[1] (numeric) = 0.7875986762734114 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.86741268935071700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.415000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 0.7936785915595413 " " y[1] (numeric) = 0.7936785915595405 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.11906561314057380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.425454545454546 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 0.7997538620343889 " " y[1] (numeric) = 0.7997538620343881 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 9.71744125449677900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.435909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 0.8058245274823892 " " y[1] (numeric) = 0.8058245274823883 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.10219829430488000000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.446363636363637 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000006 " " y[1] (analytic) = 0.8118906271790036 " " y[1] (numeric) = 0.8118906271790027 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.09396313982117440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4568181818181825 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000007 " " y[1] (analytic) = 0.8179521998993664 " " y[1] (numeric) = 0.8179521998993655 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.08585614148283830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.467272727272728 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5741812339127925 " " Order of pole (six term test) = 1.8278711877428577000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000007 " " y[1] (analytic) = 0.8240092839267467 " " y[1] (numeric) = 0.8240092839267458 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.0778742873716009000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.477727272727274 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8800000000000007 " " y[1] (analytic) = 0.8300619170608325 " " y[1] (numeric) = 0.8300619170608317 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.0700146596835540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4881818181818187 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8900000000000007 " " y[1] (analytic) = 0.8361101366258415 " " y[1] (numeric) = 0.8361101366258407 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.06227443107484320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.4986363636363644 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9000000000000007 " " y[1] (analytic) = 0.8421539794784617 " " y[1] (numeric) = 0.8421539794784608 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.05465086117643950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.50909090909091 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9100000000000007 " " y[1] (analytic) = 0.8481934820156276 " " y[1] (numeric) = 0.8481934820156267 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.04714129326893470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5195454545454554 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9200000000000007 " " y[1] (analytic) = 0.8542286801821355 " " y[1] (numeric) = 0.8542286801821346 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.03974315110884720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.530000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9300000000000007 " " y[1] (analytic) = 0.860259609478101 " " y[1] (numeric) = 0.8602596094781001 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.03245393589844570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5404545454545464 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9400000000000007 " " y[1] (analytic) = 0.8662863049662644 " " y[1] (numeric) = 0.8662863049662635 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.02527122339157090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.550909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9500000000000007 " " y[1] (analytic) = 0.8723088012791457 " " y[1] (numeric) = 0.8723088012791448 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.01819266112838540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.561363636363638 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9600000000000007 " " y[1] (analytic) = 0.8783271326260547 " " y[1] (numeric) = 0.8783271326260538 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.01121596579240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.571818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9700000000000008 " " y[1] (analytic) = 0.8843413327999583 " " y[1] (numeric) = 0.8843413327999574 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.00433892068350820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5822727272727284 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9800000000000008 " " y[1] (analytic) = 0.8903514351842094 " " y[1] (numeric) = 0.8903514351842087 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.72864451638492200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.5927272727272737 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.9900000000000008 " " y[1] (analytic) = 0.8963574727591408 " " y[1] (numeric) = 0.89635747275914 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.67015828902938600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6031818181818194 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0000000000000007 " " y[1] (analytic) = 0.9023594781085256 " " y[1] (numeric) = 0.9023594781085247 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.84284468936785800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6136363636363638 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.015129095292493 " " Order of pole (six term test) = 5.54738477376304200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0100000000000007 " " y[1] (analytic) = 0.9083574834259098 " " y[1] (numeric) = 0.908357483425909 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.55561969178182400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6240909090909095 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0200000000000007 " " y[1] (analytic) = 0.9143515205208197 " " y[1] (numeric) = 0.9143515205208189 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.49953327353726300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.634545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0300000000000007 " " y[1] (analytic) = 0.9203416208248439 " " y[1] (numeric) = 0.9203416208248432 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.44421353606820100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6450000000000005 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0400000000000007 " " y[1] (analytic) = 0.926327815397598 " " y[1] (numeric) = 0.9263278153975972 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.38964461953502900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6554545454545466 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 9.050843983951328 " " Order of pole (six term test) = 1.35884192786761560000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0500000000000007 " " y[1] (analytic) = 0.9323101349325704 " " y[1] (numeric) = 0.9323101349325696 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.33581110103257300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.665909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0600000000000007 " " y[1] (analytic) = 0.9382886097628544 " " y[1] (numeric) = 0.9382886097628538 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 7.09945541109631900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.676363636363638 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0700000000000007 " " y[1] (analytic) = 0.9442632698667689 " " y[1] (numeric) = 0.9442632698667681 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.23029066191744100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6868181818181824 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0800000000000007 " " y[1] (analytic) = 0.9502341448733683 " " y[1] (numeric) = 0.9502341448733675 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.17857494840049400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.6972727272727277 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.9019406347628744 " " Order of pole (six term test) = 1.605471311449946400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0900000000000007 " " y[1] (analytic) = 0.9562012640678483 " " y[1] (numeric) = 0.9562012640678477 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.96646030294128100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.707727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1000000000000008 " " y[1] (analytic) = 0.9621646563968458 " " y[1] (numeric) = 0.9621646563968451 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.92328293651587100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.718181818181819 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1100000000000008 " " y[1] (analytic) = 0.9681243504736373 " " y[1] (numeric) = 0.9681243504736365 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 8.02744107053396700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.728636363636364 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1200000000000008 " " y[1] (analytic) = 0.9740803745832383 " " y[1] (numeric) = 0.9740803745832374 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 9.11812251714991900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7390909090909097 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1300000000000008 " " y[1] (analytic) = 0.9800327566874051 " " y[1] (numeric) = 0.9800327566874043 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.92989940320427700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.749545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1400000000000008 " " y[1] (analytic) = 0.9859815244295429 " " y[1] (numeric) = 0.9859815244295422 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.75604763649600300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.7600000000000002 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1500000000000008 " " y[1] (analytic) = 0.9919267051395195 " " y[1] (numeric) = 0.9919267051395187 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.83481393545401700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.770454545454547 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1600000000000008 " " y[1] (analytic) = 0.9978683258383887 " " y[1] (numeric) = 0.9978683258383879 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 7.78816299820578900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.780909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1700000000000008 " " y[1] (analytic) = 1.0038064132430264 " " y[1] (numeric) = 1.0038064132430256 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.84810465426955600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.791363636363637 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1800000000000008 " " y[1] (analytic) = 1.009740993770678 " " y[1] (numeric) = 1.0097409937706774 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.59707607084019700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8018181818181818 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1900000000000008 " " y[1] (analytic) = 1.0156720935434238 " " y[1] (numeric) = 1.015672093543423 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.74473587830393900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8122727272727284 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2000000000000008 " " y[1] (analytic) = 1.0215997383925577 " " y[1] (numeric) = 1.0215997383925568 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.69399615447861300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8227272727272736 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2100000000000009 " " y[1] (analytic) = 1.027523953862889 " " y[1] (numeric) = 1.0275239538628884 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.48290302402022200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.833181818181819 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2200000000000009 " " y[1] (analytic) = 1.0334447652169634 " " y[1] (numeric) = 1.0334447652169625 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.59434823798889100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.843636363636365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2300000000000009 " " y[1] (analytic) = 1.039362197439204 " " y[1] (numeric) = 1.039362197439203 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.54541777532829700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.85409090909091 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2400000000000009 " " y[1] (analytic) = 1.0452762752399816 " " y[1] (numeric) = 1.0452762752399807 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.49706858118645400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.864545454545455 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 15.48383803931361 " " Order of pole (six term test) = 3.98893362785202040000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2500000000000009 " " y[1] (analytic) = 1.0511870230596068 " " y[1] (numeric) = 1.0511870230596059 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.44929018544173700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.875000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.260000000000001 " " y[1] (analytic) = 1.0570944650722516 " " y[1] (numeric) = 1.0570944650722505 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05025904619534050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.8854545454545466 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.270000000000001 " " y[1] (analytic) = 1.0629986251897987 " " y[1] (numeric) = 1.0629986251897976 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04442564488446630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.895909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.280000000000001 " " y[1] (analytic) = 1.0688995270656232 " " y[1] (numeric) = 1.0688995270656223 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.30927881630166600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.906363636363637 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.7841075696846556 " " Order of pole (six term test) = 2.110489560891437600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.290000000000001 " " y[1] (analytic) = 1.0747971940983054 " " y[1] (numeric) = 1.0747971940983045 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.26368383335106400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.916818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000001 " " y[1] (analytic) = 1.0806916494352765 " " y[1] (numeric) = 1.0806916494352756 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.21861092536663400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9272727272727286 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.310000000000001 " " y[1] (analytic) = 1.0865829159764004 " " y[1] (numeric) = 1.0865829159763996 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.17405102400317500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.937727272727274 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.320000000000001 " " y[1] (analytic) = 1.0924710163774924 " " y[1] (numeric) = 1.0924710163774916 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.12999527113517500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.948181818181819 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.330000000000001 " " y[1] (analytic) = 1.0983559730537735 " " y[1] (numeric) = 1.0983559730537726 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.08643501278288900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.958636363636365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.340000000000001 " " y[1] (analytic) = 1.1042378081832656 " " y[1] (numeric) = 1.1042378081832647 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.04336179324805500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9690909090909106 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.350000000000001 " " y[1] (analytic) = 1.1101165437101268 " " y[1] (numeric) = 1.1101165437101257 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0000959186813610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.9795454545454563 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.360000000000001 " " y[1] (analytic) = 1.115992201347927 " " y[1] (numeric) = 1.1159922013479262 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.95864360546030700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 2.990000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.370000000000001 " " y[1] (analytic) = 1.1218648025828695 " " y[1] (numeric) = 1.1218648025828684 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.89622833401217300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.000454545454547 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.380000000000001 " " y[1] (analytic) = 1.1277343686769505 " " y[1] (numeric) = 1.1277343686769497 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.87577681739122200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.010909090909092 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.390000000000001 " " y[1] (analytic) = 1.1336009206710722 " " y[1] (numeric) = 1.133600920671071 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.79377313815097800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.021363636363637 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000001 " " y[1] (analytic) = 1.139464479388094 " " y[1] (numeric) = 1.139464479388093 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.79470036816845500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.031818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.410000000000001 " " y[1] (analytic) = 1.1453250654358373 " " y[1] (numeric) = 1.1453250654358362 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.6935189679331500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0422727272727283 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.420000000000001 " " y[1] (analytic) = 1.1511826992100345 " " y[1] (numeric) = 1.1511826992100336 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.71535587104993600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.052727272727274 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.430000000000001 " " y[1] (analytic) = 1.1570374008972308 " " y[1] (numeric) = 1.15703740089723 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.6763155539430490000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.06318181818182 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.440000000000001 " " y[1] (analytic) = 1.1628891904776344 " " y[1] (numeric) = 1.1628891904776335 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.63768746818708500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.0736363636363646 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.450000000000001 " " y[1] (analytic) = 1.168738087727919 " " y[1] (numeric) = 1.168738087727918 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59946500440304100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.08409090909091 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.460000000000001 " " y[1] (analytic) = 1.1745841122239793 " " y[1] (numeric) = 1.1745841122239782 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.4520521184561200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.094545454545456 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.087390351546412 " " Order of pole (six term test) = 1.7461587731304462000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.470000000000001 " " y[1] (analytic) = 1.1804272833436391 " " y[1] (numeric) = 1.180427283343638 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.40526401152280800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.105000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.480000000000001 " " y[1] (analytic) = 1.1862676202693152 " " y[1] (numeric) = 1.1862676202693143 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.48716735181968800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.115454545454547 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.490000000000001 " " y[1] (analytic) = 1.1921051419906357 " " y[1] (numeric) = 1.1921051419906348 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.45050405719248400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1259090909090923 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000001 " " y[1] (analytic) = 1.1979398673070145 " " y[1] (numeric) = 1.1979398673070134 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.26776923386775100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1363636363636376 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5100000000000011 " " y[1] (analytic) = 1.203771814830183 " " y[1] (numeric) = 1.2037718148301821 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.37829552709224500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1468181818181837 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.717266718767554 " " Order of pole (six term test) = -5.7340798775840080000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5200000000000011 " " y[1] (analytic) = 1.2096010029866815 " " y[1] (numeric) = 1.2096010029866806 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.34273878334329300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.15727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5300000000000011 " " y[1] (analytic) = 1.2154274500203064 " " y[1] (numeric) = 1.2154274500203055 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.30753957947293600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.167727272727275 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5400000000000011 " " y[1] (analytic) = 1.2212511739945195 " " y[1] (numeric) = 1.2212511739945187 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.27269245355182700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.17818181818182 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5500000000000012 " " y[1] (analytic) = 1.2270721927948172 " " y[1] (numeric) = 1.227072192794816 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.0477400689561600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.1886363636363657 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.5600000000000012 " " y[1] (analytic) = 1.2328905241310593 " " y[1] (numeric) = 1.2328905241310584 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.20403314257048800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.199090909090911 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.9595335493633 " " Order of pole (six term test) = 1.1278267209036130000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5700000000000012 " " y[1] (analytic) = 1.2387061855397634 " " y[1] (numeric) = 1.2387061855397625 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.17021057994558700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2095454545454563 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.428825011803495 " " Order of pole (six term test) = 1.55040424942853860000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5800000000000012 " " y[1] (analytic) = 1.2445191943863578 " " y[1] (numeric) = 1.244519194386357 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.13671933471515800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2200000000000015 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.026157093386986 " " Order of pole (six term test) = 3.101696677276777300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.5900000000000012 " " y[1] (analytic) = 1.2503295678674005 " " y[1] (numeric) = 1.2503295678673998 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.327665856221185000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2304545454545472 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.455952258655438 " " Order of pole (six term test) = 5.12017095388728200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6000000000000012 " " y[1] (analytic) = 1.2561373230127622 " " y[1] (numeric) = 1.2561373230127615 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.303033375183981000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.240909090909093 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.413080684380695 " " Order of pole (six term test) = 2.839151136413420300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6100000000000012 " " y[1] (analytic) = 1.2619424766877727 " " y[1] (numeric) = 1.261942476687772 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.27863850437540500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2513636363636382 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6200000000000012 " " y[1] (analytic) = 1.2677450455953347 " " y[1] (numeric) = 1.267745045595334 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.254477760252470000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.261818181818184 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6300000000000012 " " y[1] (analytic) = 1.2735450462780025 " " y[1] (numeric) = 1.2735450462780018 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.230547727557047000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2722727272727297 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6400000000000012 " " y[1] (analytic) = 1.2793424951200276 " " y[1] (numeric) = 1.2793424951200267 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.9424600768600010000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2827272727272745 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 10.923780521871645 " " Order of pole (six term test) = -1.6946088976510510000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6500000000000012 " " y[1] (analytic) = 1.2851374083493725 " " y[1] (numeric) = 1.2851374083493716 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.91115528915230500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.2931818181818207 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6600000000000013 " " y[1] (analytic) = 1.2909298020396922 " " y[1] (numeric) = 1.2909298020396913 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.88014497997325300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.303636363636365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6700000000000013 " " y[1] (analytic) = 1.2967196921122843 " " y[1] (numeric) = 1.2967196921122834 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.84942493819409700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.314090909090911 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6800000000000013 " " y[1] (analytic) = 1.3025070943380084 " " y[1] (numeric) = 1.3025070943380075 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.8189910332237900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.324545454545457 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.6900000000000013 " " y[1] (analytic) = 1.3082920243391754 " " y[1] (numeric) = 1.3082920243391745 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.78883921308584300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.335000000000002 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7000000000000013 " " y[1] (analytic) = 1.3140744975914074 " " y[1] (numeric) = 1.3140744975914065 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.75896550255015700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3454545454545475 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7100000000000013 " " y[1] (analytic) = 1.3198545294254682 " " y[1] (numeric) = 1.3198545294254673 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.72936600131795300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.355909090909093 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2914854077274645 " " Order of pole (six term test) = -9.775291687219578000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7200000000000013 " " y[1] (analytic) = 1.3256321350290663 " " y[1] (numeric) = 1.3256321350290654 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.70003688225806800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.366363636363638 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7300000000000013 " " y[1] (analytic) = 1.3314073294486284 " " y[1] (numeric) = 1.3314073294486275 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.67097438969292600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3768181818181846 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7400000000000013 " " y[1] (analytic) = 1.3371801275910467 " " y[1] (numeric) = 1.3371801275910458 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.64217483773255100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3872727272727303 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7500000000000013 " " y[1] (analytic) = 1.3429505442253986 " " y[1] (numeric) = 1.3429505442253977 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.61363460865506600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.3977272727272747 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8439523498478363 " " Order of pole (six term test) = 1.50262025044867200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.7600000000000013 " " y[1] (analytic) = 1.3487185939846411 " " y[1] (numeric) = 1.3487185939846402 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.58535015133215900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.408181818181821 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7700000000000014 " " y[1] (analytic) = 1.3544842913672777 " " y[1] (numeric) = 1.3544842913672768 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.55731797969807300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.418636363636366 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7800000000000014 " " y[1] (analytic) = 1.3602476507390002 " " y[1] (numeric) = 1.3602476507389993 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.52953467126072500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4290909090909105 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.7900000000000014 " " y[1] (analytic) = 1.3660086863343073 " " y[1] (numeric) = 1.3660086863343064 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.50199686565359600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4395454545454567 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.35645133019238 " " Order of pole (six term test) = 8.89883722265949500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8000000000000014 " " y[1] (analytic) = 1.3717674122580958 " " y[1] (numeric) = 1.371767412258095 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.47470126322709200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4500000000000024 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8100000000000014 " " y[1] (analytic) = 1.37752384248723 " " y[1] (numeric) = 1.3775238424872291 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.44764462367814700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.4604545454545477 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.5728062380983283 " " Order of pole (six term test) = -1.564082197091920500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8200000000000014 " " y[1] (analytic) = 1.3832779908720865 " " y[1] (numeric) = 1.3832779908720856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.42082376471683600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.470909090909093 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8300000000000014 " " y[1] (analytic) = 1.3890298711380753 " " y[1] (numeric) = 1.3890298711380744 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.39423556076884800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.481363636363639 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8400000000000014 " " y[1] (analytic) = 1.3947794968871394 " " y[1] (numeric) = 1.3947794968871385 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.36787694171269800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.491818181818183 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8500000000000014 " " y[1] (analytic) = 1.4005268815992309 " " y[1] (numeric) = 1.40052688159923 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.3417448916505890000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.502272727272729 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8600000000000014 " " y[1] (analytic) = 1.4062720386337655 " " y[1] (numeric) = 1.4062720386337644 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.89479555963987400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.512727272727275 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8700000000000014 " " y[1] (analytic) = 1.4120149812310547 " " y[1] (numeric) = 1.4120149812310538 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.29014869888826200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.52318181818182 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.8707101645838895 " " Order of pole (six term test) = -1.741007338296185500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.8800000000000014 " " y[1] (analytic) = 1.417755722513719 " " y[1] (numeric) = 1.417755722513718 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.26467878489928500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5336363636363664 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.8900000000000015 " " y[1] (analytic) = 1.4234942754880768 " " y[1] (numeric) = 1.423494275488076 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.23942389508797500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5440909090909116 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9000000000000015 " " y[1] (analytic) = 1.429230653045516 " " y[1] (numeric) = 1.4292306530455152 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.21438126734495500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5545454545454565 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9100000000000015 " " y[1] (analytic) = 1.4349648679638436 " " y[1] (numeric) = 1.4349648679638427 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.18954818706059400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.565000000000002 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9200000000000015 " " y[1] (analytic) = 1.4406969329086157 " " y[1] (numeric) = 1.4406969329086148 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.16492198610422700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5754545454545483 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9300000000000015 " " y[1] (analytic) = 1.4464268604344492 " " y[1] (numeric) = 1.4464268604344486 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.60537503137223140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5859090909090936 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9400000000000015 " " y[1] (analytic) = 1.452154662986314 " " y[1] (numeric) = 1.4521546629863131 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.11627977610602400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.5963636363636384 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9500000000000015 " " y[1] (analytic) = 1.4578803529008044 " " y[1] (numeric) = 1.4578803529008035 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.09225865437366100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.606818181818184 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9600000000000015 " " y[1] (analytic) = 1.4636039424073954 " " y[1] (numeric) = 1.4636039424073946 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.06843418472358900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.61727272727273 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.291707643149769 " " Order of pole (six term test) = 8.46149816879915300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9700000000000015 " " y[1] (analytic) = 1.4693254436296792 " " y[1] (numeric) = 1.4693254436296783 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.04480391700054700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.627727272727276 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.9826152987231755 " " Order of pole (six term test) = 6.4641625385775110000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.9800000000000015 " " y[1] (analytic) = 1.475044868586583 " " y[1] (numeric) = 1.475044868586582 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.02136544192852600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6381818181818204 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.9900000000000015 " " y[1] (analytic) = 1.4807622291935711 " " y[1] (numeric) = 1.4807622291935703 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.99811639025821600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6486363636363652 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0000000000000013 " " y[1] (analytic) = 1.486477537263829 " " y[1] (numeric) = 1.4864775372638284 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.481290823951848400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6590909090909105 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.010000000000001 " " y[1] (analytic) = 1.4921908045094305 " " y[1] (numeric) = 1.4921908045094299 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.464132956469267000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6695454545454558 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.020000000000001 " " y[1] (analytic) = 1.4979020425424883 " " y[1] (numeric) = 1.4979020425424876 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.447111999690052700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.680000000000001 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0300000000000007 " " y[1] (analytic) = 1.503611262876288 " " y[1] (numeric) = 1.5036112628762874 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.4302262906759104000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.6904545454545468 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0400000000000005 " " y[1] (analytic) = 1.5093184769264074 " " y[1] (numeric) = 1.5093184769264067 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.41347419354208200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7009090909090925 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0500000000000003 " " y[1] (analytic) = 1.5150236960118175 " " y[1] (numeric) = 1.515023696011817 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.93123606593806500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.711363636363636 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.7645397283384097 " " Order of pole (six term test) = 3.159783545925165500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.06 " " y[1] (analytic) = 1.5207269313559713 " " y[1] (numeric) = 1.5207269313559708 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.920242948903956600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7218181818181817 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.07 " " y[1] (analytic) = 1.5264281940878732 " " y[1] (numeric) = 1.526428194087873 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.454667869638738300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7322727272727274 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.0799999999999996 " " y[1] (analytic) = 1.5321274952431383 " " y[1] (numeric) = 1.5321274952431383 " " 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 = 3.7427272727272727 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6916639192368266 " " Order of pole (six term test) = 2.024691525548405500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.0899999999999994 " " y[1] (analytic) = 1.5378248457650328 " " y[1] (numeric) = 1.537824845765033 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.44388748521337100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7531818181818184 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.099999999999999 " " y[1] (analytic) = 1.543520256505502 " " y[1] (numeric) = 1.5435202565055022 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.438559707844299400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7636363636363637 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.109999999999999 " " y[1] (analytic) = 1.5492137382261832 " " y[1] (numeric) = 1.5492137382261835 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.433272888344429800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.774090909090908 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 12.92756428279391 " " Order of pole (six term test) = 2.15129247749246130000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1199999999999988 " " y[1] (analytic) = 1.5549053015994057 " " y[1] (numeric) = 1.554905301599406 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.856053094637106500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.784545454545453 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.015291369127790 " " Order of pole (six term test) = -1.048938713665847900000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1299999999999986 " " y[1] (analytic) = 1.5605949572091753 " " y[1] (numeric) = 1.560594957209176 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.26846063866787360000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.7949999999999995 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1399999999999983 " " y[1] (analytic) = 1.5662827155521477 " " y[1] (numeric) = 1.5662827155521484 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.25296026164898140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8054545454545448 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.149999999999998 " " y[1] (analytic) = 1.5719685870385853 " " y[1] (numeric) = 1.571968587038586 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.23757713905731600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.81590909090909 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.159999999999998 " " y[1] (analytic) = 1.5776525819933038 " " y[1] (numeric) = 1.5776525819933047 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.629746560411582000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8263636363636335 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1699999999999977 " " y[1] (analytic) = 1.5833347106566047 " " y[1] (numeric) = 1.5833347106566058 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 7.01192879277401900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.83681818181818 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.210651815708611 " " Order of pole (six term test) = -3.330846709559409600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.1799999999999975 " " y[1] (analytic) = 1.5890149831851947 " " y[1] (numeric) = 1.589014983185196 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 8.38423579165783300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8472727272727254 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.1899999999999973 " " y[1] (analytic) = 1.5946934096530938 " " y[1] (numeric) = 1.5946934096530951 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 8.35438098311327800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.85772727272727 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.199999999999997 " " y[1] (analytic) = 1.6003700000525294 " " y[1] (numeric) = 1.600370000052531 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 9.71220551762531000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8681818181818155 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.209999999999997 " " y[1] (analytic) = 1.6060447642948206 " " y[1] (numeric) = 1.6060447642948221 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 9.6778886182396300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8786363636363603 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.3560652757663143 " " Order of pole (six term test) = -1.45341516599728500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2199999999999966 " " y[1] (analytic) = 1.6117177122112483 " " y[1] (numeric) = 1.61171771221125 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.10215134197608350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.8890909090909056 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.2299999999999964 " " y[1] (analytic) = 1.6173888535539154 " " y[1] (numeric) = 1.6173888535539174 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.2355726577032859000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.899545454545451 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.239999999999996 " " y[1] (analytic) = 1.6230581979965943 " " y[1] (numeric) = 1.6230581979965966 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.36806311196425280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9099999999999966 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.249999999999996 " " y[1] (analytic) = 1.628725755135564 " " y[1] (numeric) = 1.6287257551355663 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.36330259544861080000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.920454545454541 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.259999999999996 " " y[1] (analytic) = 1.6343915344904347 " " y[1] (numeric) = 1.6343915344904372 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.4944342298841240000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9309090909090862 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.492417148384499 " " Order of pole (six term test) = -6.258105145207082000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2699999999999956 " " y[1] (analytic) = 1.6400555455049637 " " y[1] (numeric) = 1.6400555455049661 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.48927312911424330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9413636363636324 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.9580214527817783 " " Order of pole (six term test) = -1.3713474800169934000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.2799999999999954 " " y[1] (analytic) = 1.6457177975478579 " " y[1] (numeric) = 1.6457177975478603 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.48414914015919900000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9518181818181772 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.289999999999995 " " y[1] (analytic) = 1.6513782999135673 " " y[1] (numeric) = 1.65137829991357 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.61352202535290480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.962272727272722 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.299999999999995 " " y[1] (analytic) = 1.6570370618230685 " " y[1] (numeric) = 1.6570370618230712 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.60801186677675150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.972727272727268 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3099999999999947 " " y[1] (analytic) = 1.6626940924246356 " " y[1] (numeric) = 1.6626940924246385 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.73608595662719360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.983181818181812 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3264615980543066 " " Order of pole (six term test) = 8.538947326997004000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3199999999999945 " " y[1] (analytic) = 1.6683494007946043 " " y[1] (numeric) = 1.6683494007946071 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.73020103741493350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 3.9936363636363583 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3299999999999943 " " y[1] (analytic) = 1.6740029959381217 " " y[1] (numeric) = 1.6740029959381248 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.85700054091500920000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.004090909090904 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.339999999999994 " " y[1] (analytic) = 1.679654886789892 " " y[1] (numeric) = 1.679654886789895 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.85075189754697280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.01454545454545 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 10.118898865929335 " " Order of pole (six term test) = 1.23579368960236020000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.349999999999994 " " y[1] (analytic) = 1.685305082214906 " " y[1] (numeric) = 1.6853050822149094 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.9763003796903940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.024999999999994 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.935155278660468 " " Order of pole (six term test) = 0.0 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.3599999999999937 " " y[1] (analytic) = 1.6909535910091678 " " y[1] (numeric) = 1.690953591009171 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.96969869048133540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.035454545454539 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3699999999999934 " " y[1] (analytic) = 1.6966004219004054 " " y[1] (numeric) = 1.6966004219004087 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.96314290087509360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.045909090909084 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.3799999999999932 " " y[1] (analytic) = 1.702245583548778 " " y[1] (numeric) = 1.7022455835487815 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0870746930615830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.0563636363636295 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.389999999999993 " " y[1] (analytic) = 1.7078890845475712 " " y[1] (numeric) = 1.7078890845475747 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0801782217266370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.066818181818175 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.399999999999993 " " y[1] (analytic) = 1.7135309334238824 " " y[1] (numeric) = 1.7135309334238862 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 2.20291224984367200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.077272727272721 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4099999999999926 " " y[1] (analytic) = 1.7191711386393007 " " y[1] (numeric) = 1.7191711386393047 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 2.3248429425205308000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.087727272727264 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4199999999999924 " " y[1] (analytic) = 1.7248097085905747 " " y[1] (numeric) = 1.724809708590579 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.44597851726090940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.098181818181810 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.429999999999992 " " y[1] (analytic) = 1.7304466516102743 " " y[1] (numeric) = 1.7304466516102786 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.4380107237918770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.108636363636355 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.439999999999992 " " y[1] (analytic) = 1.7360819759674424 " " y[1] (numeric) = 1.7360819759674466 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.4300969378042278000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.119090909090902 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4499999999999917 " " y[1] (analytic) = 1.7417156898682393 " " y[1] (numeric) = 1.7417156898682435 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 2.42223660159756050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.129545454545447 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4599999999999915 " " y[1] (analytic) = 1.7473478014565789 " " y[1] (numeric) = 1.7473478014565833 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.54150438441546940000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.139999999999990 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.4699999999999913 " " y[1] (analytic) = 1.752978318814756 " " y[1] (numeric) = 1.7529783188147607 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6600082005454670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.1504545454545365 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.479999999999991 " " y[1] (analytic) = 1.758607249964068 " " y[1] (numeric) = 1.7586072499640726 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6514940749396610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.160909090909082 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.0355602672827136 " " Order of pole (six term test) = 1.170796792848705100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.489999999999991 " " y[1] (analytic) = 1.7642346028654243 " " y[1] (numeric) = 1.764234602865429 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.6430366436823290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.171363636363627 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.863402959159726 " " Order of pole (six term test) = 2.20587992316723100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.4999999999999907 " " y[1] (analytic) = 1.7698603854199537 " " y[1] (numeric) = 1.7698603854199586 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.7600941569137260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.181818181818173 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.252914217412238 " " Order of pole (six term test) = -6.77982114893893600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5099999999999905 " " y[1] (analytic) = 1.7754846054696003 " " y[1] (numeric) = 1.7754846054696054 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.87641238766187750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.192272727272718 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5199999999999902 " " y[1] (analytic) = 1.7811072707977131 " " y[1] (numeric) = 1.7811072707977185 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.99199863229686060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.202727272727262 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.52999999999999 " " y[1] (analytic) = 1.7867283891296286 " " y[1] (numeric) = 1.786728389129634 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 2.98258568600721030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.213181818181807 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.53999999999999 " " y[1] (analytic) = 1.7923479681332453 " " y[1] (numeric) = 1.7923479681332508 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.0971190984233626000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.223636363636354 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5499999999999896 " " y[1] (analytic) = 1.7979660154195924 " " y[1] (numeric) = 1.797966015419598 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.087441628773120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.234090909090898 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1790677448576106 " " Order of pole (six term test) = -1.60227386913902600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.5599999999999894 " " y[1] (analytic) = 1.8035825385433908 " " y[1] (numeric) = 1.8035825385433963 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 3.07782704949504200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.244545454545444 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.569999999999989 " " y[1] (analytic) = 1.8091975450036062 " " y[1] (numeric) = 1.809197545003612 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.19100572737031130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.254999999999990 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 10.017569989439814 " " Order of pole (six term test) = -1.007052219392790000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.579999999999989 " " y[1] (analytic) = 1.8148110422439978 " " y[1] (numeric) = 1.8148110422440036 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 3.18113544257056850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.265454545454535 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5899999999999888 " " y[1] (analytic) = 1.8204230376536576 " " y[1] (numeric) = 1.8204230376536636 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 3.29330282520653050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.27590909090908 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.5999999999999885 " " y[1] (analytic) = 1.8260335385675455 " " y[1] (numeric) = 1.8260335385675517 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.40478354125854370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.2863636363636255 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.463519856808720 " " Order of pole (six term test) = -3.87245790989254600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6099999999999883 " " y[1] (analytic) = 1.8316425522670157 " " y[1] (numeric) = 1.8316425522670219 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 3.3943571196278527000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.296818181818170 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 7.758047699068882 " " Order of pole (six term test) = 1.17323040171868340000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.619999999999988 " " y[1] (analytic) = 1.8372500859803385 " " y[1] (numeric) = 1.837250085980345 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.50485412517477950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.307272727272715 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.629999999999988 " " y[1] (analytic) = 1.842856146883215 " " y[1] (numeric) = 1.8428561468832214 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.4941921829962436000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.317727272727260 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6399999999999877 " " y[1] (analytic) = 1.8484607420992853 " " y[1] (numeric) = 1.8484607420992918 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 3.48359767463216060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.328181818181806 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6499999999999875 " " y[1] (analytic) = 1.854063878700631 " " y[1] (numeric) = 1.8540638787006378 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.7125920157076780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.3386363636363505 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6599999999999873 " " y[1] (analytic) = 1.8596655637082722 " " y[1] (numeric) = 1.859665563708279 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.70140894524612200000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.349090909090895 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.669999999999987 " " y[1] (analytic) = 1.8652658040926566 " " y[1] (numeric) = 1.8652658040926635 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 3.6902959018349324000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.35954545454544 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5765819917431023 " " Order of pole (six term test) = 1.654143488849513200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.679999999999987 " " y[1] (analytic) = 1.8708646067741452 " " y[1] (numeric) = 1.8708646067741523 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7979377726604160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.369999999999987 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.6899999999999866 " " y[1] (analytic) = 1.8764619786234906 " " y[1] (numeric) = 1.8764619786234977 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.78660875549064140000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.380454545454530 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.4881569730611215 " " Order of pole (six term test) = 4.407141318552021400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.6999999999999864 " " y[1] (analytic) = 1.8820579264623094 " " y[1] (numeric) = 1.8820579264623167 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 3.8933296682846680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.390909090909076 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.709999999999986 " " y[1] (analytic) = 1.8876524570635511 " " y[1] (numeric) = 1.8876524570635587 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 3.99942083575869700000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.401363636363622 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.719999999999986 " " y[1] (analytic) = 1.8932455771519585 " " y[1] (numeric) = 1.8932455771519663 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.1048880642663310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.411818181818168 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7299999999999858 " " y[1] (analytic) = 1.898837293404525 " " y[1] (numeric) = 1.8988372934045328 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 4.0927999462460820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.422272727272714 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7399999999999856 " " y[1] (analytic) = 1.9044276124509447 " " y[1] (numeric) = 1.9044276124509527 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.1973796877548847000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.4327272727272575 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.636415412513885 " " Order of pole (six term test) = 1.953814887656335500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.7499999999999853 " " y[1] (analytic) = 1.9100165408740595 " " y[1] (numeric) = 1.9100165408740675 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.18509767127100530000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.443181818181804 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.759999999999985 " " y[1] (analytic) = 1.9156040852102978 " " y[1] (numeric) = 1.9156040852103058 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 4.17289033731809870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.453636363636348 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.769999999999985 " " y[1] (analytic) = 1.9211902519501112 " " y[1] (numeric) = 1.9211902519501194 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 4.27633357700354400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.464090909090895 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7799999999999847 " " y[1] (analytic) = 1.926775047538404 " " y[1] (numeric) = 1.9267750475384124 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.37918012169140450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.4745454545454395 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7899999999999845 " " y[1] (analytic) = 1.932358478374959 " " y[1] (numeric) = 1.9323584783749674 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 4.3665267503817280000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.484999999999984 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.7999999999999843 " " y[1] (analytic) = 1.9379405508148566 " " y[1] (numeric) = 1.9379405508148653 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.4685269568434450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.495454545454530 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.809999999999984 " " y[1] (analytic) = 1.9435212711688916 " " y[1] (numeric) = 1.9435212711689003 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 4.4556958138502880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.505909090909074 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.705123936737315 " " Order of pole (six term test) = 1.041122743572486800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.819999999999984 " " y[1] (analytic) = 1.9491006457039821 " " y[1] (numeric) = 1.949100645703991 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.5568627851915270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.51636363636362 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.486190114591166 " " Order of pole (six term test) = 6.41993125327644500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8299999999999836 " " y[1] (analytic) = 1.954678680643577 " " y[1] (numeric) = 1.9546786806435859 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 4.5438589395556966000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.5268181818181645 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5987864190881573 " " Order of pole (six term test) = 1.753797107539867300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.8399999999999834 " " y[1] (analytic) = 1.9602553821680555 " " y[1] (numeric) = 1.9602553821680646 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 4.644205487071480000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.53727272727271 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.849999999999983 " " y[1] (analytic) = 1.9658307564151252 " " y[1] (numeric) = 1.9658307564151345 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 4.7439859084603553000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.547727272727255 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.859999999999983 " " y[1] (analytic) = 1.9714048094802126 " " y[1] (numeric) = 1.9714048094802221 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.843205193505530400000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.558181818181800 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.869999999999983 " " y[1] (analytic) = 1.9769775474168516 " " y[1] (numeric) = 1.9769775474168612 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 4.8295530843290550000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.568636363636346 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8799999999999826 " " y[1] (analytic) = 1.9825489762370654 " " y[1] (numeric) = 1.9825489762370752 " " absolute error = 9.769962616701378000000000000000E-15 " " relative error = 4.9279804604096320000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.579090909090891 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.8899999999999824 " " y[1] (analytic) = 1.9881191019117466 " " y[1] (numeric) = 1.9881191019117566 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0258594729149970000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.589545454545437 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 21.342297213533353 " " Order of pole (six term test) = 2.35878871990280460000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.899999999999982 " " y[1] (analytic) = 1.9936879303710304 " " y[1] (numeric) = 1.9936879303710404 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 5.0118210926656260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.599999999999982 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.909999999999982 " " y[1] (analytic) = 1.999255467504665 " " y[1] (numeric) = 1.9992554675046752 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.1089277946554410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.610454545454527 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 9.888034670642462 " " Order of pole (six term test) = 1.3254286557184970000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9199999999999817 " " y[1] (analytic) = 2.004821719162378 " " y[1] (numeric) = 2.004821719162388 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.0947432028115260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.620909090909073 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9299999999999815 " " y[1] (analytic) = 2.0103866911542374 " " y[1] (numeric) = 2.0103866911542476 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 5.0806403919671660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.631363636363617 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9399999999999813 " " y[1] (analytic) = 2.0159503892510093 " " y[1] (numeric) = 2.01595038925102 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.2869064106093130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.641818181818163 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.852836310453656 " " Order of pole (six term test) = 8.94040397270146100000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.949999999999981 " " y[1] (analytic) = 2.021512819184513 " " y[1] (numeric) = 2.0215128191845237 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.2723588667130210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.652272727272707 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.433422028684825 " " Order of pole (six term test) = 3.53050921830799800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.959999999999981 " " y[1] (analytic) = 2.027073986647969 " " y[1] (numeric) = 2.02707398664798 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4769733711646850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.662727272727254 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9699999999999807 " " y[1] (analytic) = 2.032633897296345 " " y[1] (numeric) = 2.032633897296356 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4619920788583260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.673181818181800 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 28.90653359588314 " " Order of pole (six term test) = -4.4399151022389560000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.9799999999999804 " " y[1] (analytic) = 2.038192556746699 " " y[1] (numeric) = 2.03819255674671 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4470958641771350000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.683636363636344 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.9899999999999802 " " y[1] (analytic) = 2.0437499705785163 " " y[1] (numeric) = 2.0437499705785274 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4322839907412460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.694090909090888 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.99999999999998 " " y[1] (analytic) = 2.049306144334044 " " y[1] (numeric) = 2.049306144334055 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4175557307272990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.704545454545434 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00999999999998 " " y[1] (analytic) = 2.054861083518622 " " y[1] (numeric) = 2.054861083518633 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 5.4029103647438630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.7149999999999785 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0199999999999796 " " y[1] (analytic) = 2.06041479360101 " " y[1] (numeric) = 2.0604147936010215 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.6038810689773770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.725454545454525 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0299999999999794 " " y[1] (analytic) = 2.0659672800137105 " " y[1] (numeric) = 2.065967280013722 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.5888200978792860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.735909090909070 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.039999999999979 " " y[1] (analytic) = 2.071518548153289 " " y[1] (numeric) = 2.0715185481533007 " " absolute error = 1.154631945610162800000000000000E-14 " " relative error = 5.5738431434248580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.746363636363615 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.049999999999979 " " y[1] (analytic) = 2.0770686033806895 " " y[1] (numeric) = 2.0770686033807015 " " absolute error = 1.19904086659516900000000000000E-14 " " relative error = 5.7727552409370570000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.756818181818161 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 9.51488382379298 " " Order of pole (six term test) = 1.15313980586506660000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0599999999999787 " " y[1] (analytic) = 2.082617451021548 " " y[1] (numeric) = 2.0826174510215605 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9706106225617610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.767272727272705 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.0699999999999785 " " y[1] (analytic) = 2.088165096366503 " " y[1] (numeric) = 2.0881650963665153 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9547484523318170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.777727272727251 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.424385251902450 " " Order of pole (six term test) = 3.398170633772679000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.0799999999999783 " " y[1] (analytic) = 2.0937115446714976 " " y[1] (numeric) = 2.0937115446715104 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.1510799414694250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.788181818181797 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.089999999999978 " " y[1] (analytic) = 2.099256801158088 " " y[1] (numeric) = 2.0992568011581003 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9232857404306460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.7986363636363425 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3042232468286317 " " Order of pole (six term test) = -3.45909967336410800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.099999999999978 " " y[1] (analytic) = 2.1048008710137367 " " y[1] (numeric) = 2.104800871013749 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 5.9076837372330230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.809090909090886 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1099999999999777 " " y[1] (analytic) = 2.110343759392113 " " y[1] (numeric) = 2.110343759392126 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.1026015445756130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.819545454545431 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1199999999999775 " " y[1] (analytic) = 2.1158854714133857 " " y[1] (numeric) = 2.1158854714133986 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.0866182313020360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.829999999999977 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3395626866595298 " " Order of pole (six term test) = 6.9544370262519810000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1299999999999772 " " y[1] (analytic) = 2.1214260121645094 " " y[1] (numeric) = 2.1214260121645223 " " absolute error = 1.287858708565181600000000000000E-14 " " relative error = 6.0707217747894400000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.840454545454523 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 0.9485455689187827 " " Order of pole (six term test) = 1.710986907710321200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.139999999999977 " " y[1] (analytic) = 2.1269653866995144 " " y[1] (numeric) = 2.1269653866995277 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2637015058224030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.8509090909090675 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.149999999999977 " " y[1] (analytic) = 2.1325036000397897 " " y[1] (numeric) = 2.132503600039803 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2474343749071730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.861363636363614 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1599999999999766 " " y[1] (analytic) = 2.138040657174362 " " y[1] (numeric) = 2.1380406571743755 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2312548878790490000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.871818181818156 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.1699999999999764 " " y[1] (analytic) = 2.143576563060175 " " y[1] (numeric) = 2.143576563060188 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.2151623250080680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.882272727272704 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.179999999999976 " " y[1] (analytic) = 2.149111322622362 " " y[1] (numeric) = 2.1491113226223755 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 6.1991559745008670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.892727272727249 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.189999999999976 " " y[1] (analytic) = 2.15464494075452 " " y[1] (numeric) = 2.1546449407545336 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.389342970137369000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.903181818181794 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 20.393505044231546 " " Order of pole (six term test) = 4.0784442489893990000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.1999999999999758 " " y[1] (analytic) = 2.1601774223189762 " " y[1] (numeric) = 2.16017742231899 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 6.3729790725120870000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.913636363636340 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2099999999999755 " " y[1] (analytic) = 2.1657087721470543 " " y[1] (numeric) = 2.1657087721470685 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5617570090523090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.924090909090884 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2199999999999753 " " y[1] (analytic) = 2.1712389950393387 " " y[1] (numeric) = 2.171238995039353 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5450439807270180000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.93454545454543 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.229999999999975 " " y[1] (analytic) = 2.176768095765933 " " y[1] (numeric) = 2.176768095765947 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.5284192389826770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.9449999999999745 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.239999999999975 " " y[1] (analytic) = 2.1822960790667185 " " y[1] (numeric) = 2.182296079066733 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.7153783877572670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.95545454545452 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2499999999999747 " " y[1] (analytic) = 2.18782294965161 " " y[1] (numeric) = 2.187822949651624 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 6.4954317795527950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.965909090909066 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2599999999999745 " " y[1] (analytic) = 2.1933487122008044 " " y[1] (numeric) = 2.193348712200819 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.6815385276093680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.976363636363609 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2699999999999743 " " y[1] (analytic) = 2.1988733713650346 " " y[1] (numeric) = 2.1988733713650492 " " absolute error = 1.465494392505206600000000000000E-14 " " relative error = 6.6647511929959170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.986818181818155 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.279999999999974 " " y[1] (analytic) = 2.204396931765813 " " y[1] (numeric) = 2.204396931765828 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.8495074173448330000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 4.997272727272701 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.289999999999974 " " y[1] (analytic) = 2.209919397995678 " " y[1] (numeric) = 2.209919397995693 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 6.8323908775118410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.007727272727247 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.2999999999999736 " " y[1] (analytic) = 2.215440774618433 " " y[1] (numeric) = 2.2154407746184486 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 7.0158148765810250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.018181818181793 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3099999999999734 " " y[1] (analytic) = 2.220961066169389 " " y[1] (numeric) = 2.2209610661694046 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9983767754921760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.028636363636336 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.319999999999973 " " y[1] (analytic) = 2.226480277155599 " " y[1] (numeric) = 2.2264802771556145 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9810285337937230000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.039090909090880 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.329999999999973 " " y[1] (analytic) = 2.231998412056092 " " y[1] (numeric) = 2.2319984120561074 " " absolute error = 1.55431223447521920000000000000E-14 " " relative error = 6.9637694457112290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.049545454545426 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3399999999999728 " " y[1] (analytic) = 2.2375154753221063 " " y[1] (numeric) = 2.2375154753221222 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1450730647128960000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.059999999999972 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3499999999999726 " " y[1] (analytic) = 2.243031471377319 " " y[1] (numeric) = 2.243031471377335 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1275021142638760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.070454545454519 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.233072873628456 " " Order of pole (six term test) = 1.031885688007605500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3599999999999723 " " y[1] (analytic) = 2.2485464046180716 " " y[1] (numeric) = 2.2485464046180876 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.1100207324019060000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.080909090909063 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.369999999999972 " " y[1] (analytic) = 2.2540602794135953 " " y[1] (numeric) = 2.2540602794136118 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2896456738623680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.0913636363636074 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.379999999999972 " " y[1] (analytic) = 2.259573100106235 " " y[1] (numeric) = 2.259573100106251 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 7.0753238980631370000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.101818181818153 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.3899999999999717 " " y[1] (analytic) = 2.265084871011666 " " y[1] (numeric) = 2.265084871011682 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2541656053327150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.112272727272698 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 7.021834054591372 " " Order of pole (six term test) = 5.47686340723885200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.3999999999999715 " " y[1] (analytic) = 2.270595596419116 " " y[1] (numeric) = 2.2705955964191324 " " absolute error = 1.643130076445231700000000000000E-14 " " relative error = 7.2365597776925130000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.122727272727245 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.80674167777553 " " Order of pole (six term test) = -4.109246276584599400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4099999999999713 " " y[1] (analytic) = 2.276105280591578 " " y[1] (numeric) = 2.2761052805915947 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.4141517609925010000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.1331818181817885 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2775915351401483 " " Order of pole (six term test) = -2.05044869971970900000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.419999999999971 " " y[1] (analytic) = 2.2816139277660246 " " y[1] (numeric) = 2.2816139277660414 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.3962512977931470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.143636363636334 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.429999999999971 " " y[1] (analytic) = 2.2871215421536197 " " y[1] (numeric) = 2.287121542153637 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5726098788103410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.15409090909088 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0241947809329592 " " Order of pole (six term test) = 4.201083925181592300000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.4399999999999706 " " y[1] (analytic) = 2.292628127939928 " " y[1] (numeric) = 2.292628127939945 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 7.360718368864291000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.164545454545425 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4499999999999704 " " y[1] (analytic) = 2.2981336892851196 " " y[1] (numeric) = 2.298133689285137 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5363236111559770000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.1749999999999705 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.45999999999997 " " y[1] (analytic) = 2.303638230324179 " " y[1] (numeric) = 2.3036382303241965 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5183155741060780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.1854545454545145 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.46999999999997 " " y[1] (analytic) = 2.3091417551671043 " " y[1] (numeric) = 2.3091417551671216 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.5003966930125050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.19590909090906 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.282757909443429 " " Order of pole (six term test) = 1.003996885629021600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.47999999999997 " " y[1] (analytic) = 2.3146442678991104 " " y[1] (numeric) = 2.3146442678991277 " " absolute error = 1.731947918415244200000000000000E-14 " " relative error = 7.4825662951104310000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.206363636363606 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4899999999999696 " " y[1] (analytic) = 2.3201457725808265 " " y[1] (numeric) = 2.3201457725808443 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 7.6562294507224450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.216818181818152 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.4999999999999694 " " y[1] (analytic) = 2.325646273248495 " " y[1] (numeric) = 2.3256462732485126 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 7.6381213249554520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.227272727272696 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.0972285998920923 " " Order of pole (six term test) = -1.400657367867097500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.509999999999969 " " y[1] (analytic) = 2.3311457739141628 " " y[1] (numeric) = 2.331145773914181 " " absolute error = 1.820765760385256700000000000000E-14 " " relative error = 7.8106044708137610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.23772727272724 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.519999999999969 " " y[1] (analytic) = 2.3366442785658785 " " y[1] (numeric) = 2.336644278565897 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9822791106013740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.248181818181787 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.915337468609237 " " Order of pole (six term test) = 1.58131285843410300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5299999999999687 " " y[1] (analytic) = 2.3421417911678812 " " y[1] (numeric) = 2.3421417911679 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9635429776444730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.258636363636332 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5399999999999685 " " y[1] (analytic) = 2.3476383156607885 " " y[1] (numeric) = 2.347638315660807 " " absolute error = 1.86517468137026300000000000000E-14 " " relative error = 7.9448979381871830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.269090909090877 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.873538677207344 " " Order of pole (six term test) = 3.35944605467375370000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5499999999999683 " " y[1] (analytic) = 2.353133855961786 " " y[1] (numeric) = 2.353133855961805 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.1150657771432790000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.279545454545422 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.559999999999968 " " y[1] (analytic) = 2.3586284159648123 " " y[1] (numeric) = 2.3586284159648314 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0961612665644990000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.289999999999967 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.569999999999968 " " y[1] (analytic) = 2.3641219995407416 " " y[1] (numeric) = 2.3641219995407607 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0773479656558680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.300454545454513 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.5799999999999677 " " y[1] (analytic) = 2.369614610537566 " " y[1] (numeric) = 2.3696146105375853 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0586252037079780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.310909090909057 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 7.032917428461847 " " Order of pole (six term test) = 5.44826406212450800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5899999999999674 " " y[1] (analytic) = 2.375106252780576 " " y[1] (numeric) = 2.3751062527805953 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0399923166371520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.321363636363603 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.063200947263436 " " Order of pole (six term test) = 9.087841590371681000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.5999999999999672 " " y[1] (analytic) = 2.3805969300725383 " " y[1] (numeric) = 2.3805969300725573 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0214486469033750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.331818181818148 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 22.19486614850307 " " Order of pole (six term test) = 4.28620694492565240000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.609999999999967 " " y[1] (analytic) = 2.3860866461938715 " " y[1] (numeric) = 2.3860866461938905 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 8.0029935434294120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.342272727272692 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.619999999999967 " " y[1] (analytic) = 2.3915754049028224 " " y[1] (numeric) = 2.3915754049028415 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 7.984626361521150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.352727272727238 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.004307615896770 " " Order of pole (six term test) = 1.60369495461054600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.6299999999999666 " " y[1] (analytic) = 2.3970632099356375 " " y[1] (numeric) = 2.397063209935657 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1516103340167710000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.3631818181817845 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6399999999999664 " " y[1] (analytic) = 2.402550065006736 " " y[1] (numeric) = 2.4025500650067557 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1329939875146660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.373636363636330 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.649999999999966 " " y[1] (analytic) = 2.408035973808879 " " y[1] (numeric) = 2.4080359738088983 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.1144656665970560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.384090909090875 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.659999999999966 " " y[1] (analytic) = 2.4135209400133357 " " y[1] (numeric) = 2.413520940013355 " " absolute error = 1.909583602355269200000000000000E-14 " " relative error = 7.9120241747093270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.39454545454542 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6699999999999657 " " y[1] (analytic) = 2.4190049672700518 " " y[1] (numeric) = 2.4190049672700713 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.0776705702487150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.404999999999966 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6799999999999655 " " y[1] (analytic) = 2.4244880592078153 " " y[1] (numeric) = 2.424488059207835 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.059402544464290000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.415454545454509 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.6899999999999653 " " y[1] (analytic) = 2.4299702194344164 " " y[1] (numeric) = 2.4299702194344364 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.2239750443954670000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.425909090909056 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.699999999999965 " " y[1] (analytic) = 2.435451451536813 " " y[1] (numeric) = 2.4354514515368324 " " absolute error = 1.953992523340275500000000000000E-14 " " relative error = 8.0231224568540340000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.4363636363636 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.709999999999965 " " y[1] (analytic) = 2.440931759081286 " " y[1] (numeric) = 2.4409317590813058 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1870434799760120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.446818181818145 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7199999999999647 " " y[1] (analytic) = 2.4464111456136037 " " y[1] (numeric) = 2.4464111456136237 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1687064249539590000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.457272727272690 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7299999999999645 " " y[1] (analytic) = 2.4518896146591747 " " y[1] (numeric) = 2.4518896146591946 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1504543776252750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.4677272727272355 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7399999999999642 " " y[1] (analytic) = 2.4573671697232045 " " y[1] (numeric) = 2.4573671697232244 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.1322867373961860000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.478181818181783 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.749999999999964 " " y[1] (analytic) = 2.4628438142908498 " " y[1] (numeric) = 2.4628438142908697 " " absolute error = 1.998401444325281800000000000000E-14 " " relative error = 8.11420290937410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.488636363636328 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.759999999999964 " " y[1] (analytic) = 2.468319551827371 " " y[1] (numeric) = 2.4683195518273915 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2761179110619380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.499090909090870 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 20.44040460023301 " " Order of pole (six term test) = 3.4451375086064220000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.7699999999999636 " " y[1] (analytic) = 2.4737943857782843 " " y[1] (numeric) = 2.4737943857783047 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2578017682241460000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.5095454545454166 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.7799999999999634 " " y[1] (analytic) = 2.479268319569509 " " y[1] (numeric) = 2.4792683195695293 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2395695100278390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.519999999999961 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.789999999999963 " " y[1] (analytic) = 2.4847413566075183 " " y[1] (numeric) = 2.4847413566075387 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2214205509880110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.530454545454508 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.799999999999963 " " y[1] (analytic) = 2.490213500279485 " " y[1] (numeric) = 2.4902135002795056 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.2033543111103390000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.540909090909054 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8099999999999627 " " y[1] (analytic) = 2.495684753953428 " " y[1] (numeric) = 2.4956847539534484 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1853702158265820000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.5513636363635985 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 17.10915032838831 " " Order of pole (six term test) = 2.49166021148994330000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8199999999999625 " " y[1] (analytic) = 2.5011551209783542 " " y[1] (numeric) = 2.5011551209783747 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1674676959309120000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.5618181818181425 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8299999999999623 " " y[1] (analytic) = 2.5066246046844043 " " y[1] (numeric) = 2.5066246046844247 " " absolute error = 2.04281036531028800000000000000E-14 " " relative error = 8.1496461875171270000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.57227272727269 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.839999999999962 " " y[1] (analytic) = 2.5120932083829914 " " y[1] (numeric) = 2.5120932083830123 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 8.3086856782627740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.582727272727233 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.849999999999962 " " y[1] (analytic) = 2.5175609353669444 " " y[1] (numeric) = 2.5175609353669652 " " absolute error = 2.087219286295294300000000000000E-14 " " relative error = 8.2906405838040780000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.59318181818178 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8599999999999617 " " y[1] (analytic) = 2.523027788910643 " " y[1] (numeric) = 2.5230277889106643 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4486909603190090000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.603636363636324 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9795207657203466 " " Order of pole (six term test) = 2.3234747459355276000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.8699999999999615 " " y[1] (analytic) = 2.5284937722701586 " " y[1] (numeric) = 2.52849377227018 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4304269627148810000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.614090909090868 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.8799999999999613 " " y[1] (analytic) = 2.5339588886833884 " " y[1] (numeric) = 2.5339588886834097 " " absolute error = 2.131628207280300600000000000000E-14 " " relative error = 8.4122446374331930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.624545454545414 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.889999999999961 " " y[1] (analytic) = 2.5394231413701913 " " y[1] (numeric) = 2.539423141370213 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.5690214159865730000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.634999999999960 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.899999999999961 " " y[1] (analytic) = 2.544886533532522 " " y[1] (numeric) = 2.544886533532544 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.5506253406307250000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.645454545454506 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9099999999999606 " " y[1] (analytic) = 2.550349068354562 " " y[1] (numeric) = 2.5503490683545844 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.7064397450616580000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.65590909090905 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9199999999999604 " " y[1] (analytic) = 2.5558107490028537 " " y[1] (numeric) = 2.5558107490028754 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 8.514077691841170000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.666363636363594 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.240325107458447 " " Order of pole (six term test) = -6.7856831265089570000000000000E-13 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.92999999999996 " " y[1] (analytic) = 2.5612715786264255 " " y[1] (numeric) = 2.5612715786264477 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.6693112428206750000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.676818181818142 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.93999999999996 " " y[1] (analytic) = 2.5667315603569274 " " y[1] (numeric) = 2.5667315603569496 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 8.6508697814178110000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.687272727272686 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9499999999999598 " " y[1] (analytic) = 2.5721906973087525 " " y[1] (numeric) = 2.572190697308775 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.80515963534510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.697727272727230 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9599999999999596 " " y[1] (analytic) = 2.5776489925791677 " " y[1] (numeric) = 2.5776489925791903 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7865142878477410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.708181818181776 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9699999999999593 " " y[1] (analytic) = 2.5831064492484366 " " y[1] (numeric) = 2.5831064492484592 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7679505848250520000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.718636363636321 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.979999999999959 " " y[1] (analytic) = 2.588563070379945 " " y[1] (numeric) = 2.588563070379968 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.7494679814886160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.729090909090867 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.989999999999959 " " y[1] (analytic) = 2.5940188590203235 " " y[1] (numeric) = 2.5940188590203466 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.9022633092669930000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.739545454545412 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.9999999999999587 " " y[1] (analytic) = 2.59947381819957 " " y[1] (numeric) = 2.599473818199593 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8835820351510690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.749999999999957 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 3.2812398104841454 " " Order of pole (six term test) = 2.91358048798429100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.009999999999959 " " y[1] (analytic) = 2.60492795093117 " " y[1] (numeric) = 2.6049279509311924 " " absolute error = 2.264854970235319300000000000000E-14 " " relative error = 8.6945013946574360000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.760454545454503 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.019999999999959 " " y[1] (analytic) = 2.6103812602122147 " " y[1] (numeric) = 2.610381260212238 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8464621104144410000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.77090909090905 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.0299999999999585 " " y[1] (analytic) = 2.6158337490235244 " " y[1] (numeric) = 2.6158337490235475 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8280223927929690000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.781363636363594 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.039999999999958 " " y[1] (analytic) = 2.6212854203297615 " " y[1] (numeric) = 2.6212854203297846 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.8096621348842540000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.79181818181814 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.049999999999958 " " y[1] (analytic) = 2.6267362770795493 " " y[1] (numeric) = 2.6267362770795724 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7913808149320760000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.802272727272685 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.059999999999958 " " y[1] (analytic) = 2.632186322205586 " " y[1] (numeric) = 2.632186322205609 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7731779157841890000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.812727272727229 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.4970907457987845 " " Order of pole (six term test) = 1.63815627729491100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.069999999999958 " " y[1] (analytic) = 2.6376355586247615 " " y[1] (numeric) = 2.6376355586247846 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7550529248413470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.823181818181775 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3093660761896304 " " Order of pole (six term test) = -1.021938089706964100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.079999999999957 " " y[1] (analytic) = 2.643083989238268 " " y[1] (numeric) = 2.643083989238291 " " absolute error = 2.309263891220325600000000000000E-14 " " relative error = 8.7370053340070030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.833636363636319 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.089999999999957 " " y[1] (analytic) = 2.648531616931715 " " y[1] (numeric) = 2.6485316169317383 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 8.8867083827076510000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.844090909090864 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.099999999999957 " " y[1] (analytic) = 2.653978444575239 " " y[1] (numeric) = 2.6539784445752623 " " absolute error = 2.35367281220533200000000000000E-14 " " relative error = 8.8684699644651030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.85454545454541 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.109999999999957 " " y[1] (analytic) = 2.659424475023614 " " y[1] (numeric) = 2.6594244750236378 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 9.0172958687576380000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.864999999999956 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 23.38109520027063 " " Order of pole (six term test) = 4.35795399766902850000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.119999999999957 " " y[1] (analytic) = 2.6648697111163626 " " y[1] (numeric) = 2.6648697111163866 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.9988704632983260000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.875454545454500 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.129999999999956 " " y[1] (analytic) = 2.6703141556778625 " " y[1] (numeric) = 2.6703141556778864 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.9805228650393840000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.885909090909045 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.139999999999956 " " y[1] (analytic) = 2.6757578115174545 " " y[1] (numeric) = 2.6757578115174785 " " absolute error = 2.39808173319033800000000000000E-14 " " relative error = 8.962252573338680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.896363636363590 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.149999999999956 " " y[1] (analytic) = 2.6812006814295497 " " y[1] (numeric) = 2.681200681429574 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 9.1096898158069560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.906818181818136 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.305457419902332 " " Order of pole (six term test) = -3.66533470241847700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.159999999999956 " " y[1] (analytic) = 2.6866427681937353 " " y[1] (numeric) = 2.6866427681937597 " " absolute error = 2.442490654175344400000000000000E-14 " " relative error = 9.0912371495428190000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.917272727272683 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 28.972480165491774 " " Order of pole (six term test) = 6.6570926549047730000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.1699999999999555 " " y[1] (analytic) = 2.6920840745748773 " " y[1] (numeric) = 2.692084074574902 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2378228401097440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.9277272727272265 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.179999999999955 " " y[1] (analytic) = 2.697524603323227 " " y[1] (numeric) = 2.697524603323252 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2191914472127680000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.938181818181773 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.189999999999955 " " y[1] (analytic) = 2.7029643571745217 " " y[1] (numeric) = 2.7029643571745465 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.2006376945346440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.948636363636316 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.199999999999955 " " y[1] (analytic) = 2.708403338850088 " " y[1] (numeric) = 2.708403338850113 " " absolute error = 2.486899575160350700000000000000E-14 " " relative error = 9.182161089109491000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.959090909090861 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.209999999999955 " " y[1] (analytic) = 2.7138415510569414 " " y[1] (numeric) = 2.7138415510569667 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.3273997340025440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.969545454545408 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.2199999999999545 " " y[1] (analytic) = 2.7192789964878883 " " y[1] (numeric) = 2.7192789964879136 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.3087487507339030000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.979999999999955 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.229999999999954 " " y[1] (analytic) = 2.7247156778216235 " " y[1] (numeric) = 2.724715677821649 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.2901748125481720000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 5.990454545454497 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.239999999999954 " " y[1] (analytic) = 2.73015159772283 " " y[1] (numeric) = 2.7301515977228554 " " absolute error = 2.53130849614535700000000000000E-14 " " relative error = 9.2716774345302850000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.000909090909044 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.249999999999954 " " y[1] (analytic) = 2.7355867588422758 " " y[1] (numeric) = 2.7355867588423015 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.4155939628119470000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.011363636363588 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.259999999999954 " " y[1] (analytic) = 2.741021163816911 " " y[1] (numeric) = 2.741021163816937 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.396926412431050000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.0218181818181336 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.269999999999953 " " y[1] (analytic) = 2.746454815269963 " " y[1] (numeric) = 2.746454815269989 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.3783353099773560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.032272727272678 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.688781607846945 " " Order of pole (six term test) = 1.171862606952345200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.279999999999953 " " y[1] (analytic) = 2.7518877158110326 " " y[1] (numeric) = 2.7518877158110584 " " absolute error = 2.575717417130363000000000000000E-14 " " relative error = 9.3598201784597560000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.042727272727224 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.289999999999953 " " y[1] (analytic) = 2.757319868036187 " " y[1] (numeric) = 2.757319868036213 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 9.5024388301436740000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.05318181818177 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.299999999999953 " " y[1] (analytic) = 2.7627512745280542 " " y[1] (numeric) = 2.7627512745280804 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 9.4837575943674160000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.0636363636363155 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3099999999999525 " " y[1] (analytic) = 2.7681819378559154 " " y[1] (numeric) = 2.768181937855942 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 9.6255785165774950000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.07409090909086 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.319999999999952 " " y[1] (analytic) = 2.773611860575797 " " y[1] (numeric) = 2.7736118605758238 " " absolute error = 2.664535259100375700000000000000E-14 " " relative error = 9.6067344424580830000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.084545454545405 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.539096050037581 " " Order of pole (six term test) = -2.6965096822095800000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.329999999999952 " " y[1] (analytic) = 2.7790410452305605 " " y[1] (numeric) = 2.7790410452305876 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 9.7477659955203610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.094999999999950 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.339999999999952 " " y[1] (analytic) = 2.7844694943499944 " " y[1] (numeric) = 2.7844694943500214 " " absolute error = 2.70894418008538200000000000000E-14 " " relative error = 9.7287622851754640000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.105454545454494 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 7.269267207075873 " " Order of pole (six term test) = 7.8754780474810100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.349999999999952 " " y[1] (analytic) = 2.7898972104509014 " " y[1] (numeric) = 2.789897210450929 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 9.8690127032507880000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.115909090909042 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.3599999999999515 " " y[1] (analytic) = 2.7953241960371904 " " y[1] (numeric) = 2.795324196037218 " " absolute error = 2.753353101070388000000000000000E-14 " " relative error = 9.84985249644279900000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.126363636363587 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.34547922294145 " " Order of pole (six term test) = 1.53139723124695600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.369999999999951 " " y[1] (analytic) = 2.800750453599961 " " y[1] (numeric) = 2.800750453599989 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9893298899917150000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.136818181818132 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.379999999999951 " " y[1] (analytic) = 2.8061759856175934 " " y[1] (numeric) = 2.8061759856176214 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9700162655324440000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.147272727272675 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.389999999999950 " " y[1] (analytic) = 2.8116007945558334 " " y[1] (numeric) = 2.8116007945558614 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9507797389756210000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.157727272727220 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 32.65008027516825 " " Order of pole (six term test) = 4.1995562582997080000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.399999999999950 " " y[1] (analytic) = 2.817024882867878 " " y[1] (numeric) = 2.817024882867906 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9316198414517630000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.168181818181767 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40999999999995 " " y[1] (analytic) = 2.822448252994461 " " y[1] (numeric) = 2.822448252994489 " " absolute error = 2.797762022055394500000000000000E-14 " " relative error = 9.9125361079237660000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.178636363636313 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.41999999999995 " " y[1] (analytic) = 2.8278709073639376 " " y[1] (numeric) = 2.827870907363966 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.005056820535628000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.189090909090858 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.42999999999995 " " y[1] (analytic) = 2.8332928483923676 " " y[1] (numeric) = 2.833292848392396 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.0031334899437136000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.199545454545402 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.3273933627778387 " " Order of pole (six term test) = 1.97886151909187900000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.43999999999995 " " y[1] (analytic) = 2.8387140784835974 " " y[1] (numeric) = 2.838714078483626 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 1.0012177572172572000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.2099999999999485 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4499999999999496 " " y[1] (analytic) = 2.8441346000293435 " " y[1] (numeric) = 2.844134600029372 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.9930957663223020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.220454545454494 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.459999999999950 " " y[1] (analytic) = 2.8495544154092736 " " y[1] (numeric) = 2.849554415409302 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.974089028344411000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.230909090909038 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.6831569186682005 " " Order of pole (six term test) = 1.853095454862341300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.469999999999950 " " y[1] (analytic) = 2.8549735269910865 " " y[1] (numeric) = 2.854973526991115 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 9.955156908357821000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.241363636363584 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.165163844217659 " " Order of pole (six term test) = -2.31246133353124600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.479999999999949 " " y[1] (analytic) = 2.8603919371305935 " " y[1] (numeric) = 2.8603919371306223 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.0091553631356841000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.251818181818129 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.489999999999949 " " y[1] (analytic) = 2.865809648171798 " " y[1] (numeric) = 2.865809648171827 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.0072475908743132000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.262272727272673 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.4999999999999485 " " y[1] (analytic) = 2.871226662446972 " " y[1] (numeric) = 2.8712266624470013 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0208141430786623000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.272727272727221 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.509999999999948 " " y[1] (analytic) = 2.876642982276737 " " y[1] (numeric) = 2.8766429822767665 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0188920916041738000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.283181818181766 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 22.801644677689655 " " Order of pole (six term test) = 1.9143264751164680000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.519999999999948 " " y[1] (analytic) = 2.882058609970141 " " y[1] (numeric) = 2.8820586099701697 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 1.0015687585393392000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.293636363636310 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.529999999999948 " " y[1] (analytic) = 2.8874735478247318 " " y[1] (numeric) = 2.8874735478247606 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9969049628177610000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.304090909090854 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 5.175974424573998 " " Order of pole (six term test) = 2.976285884415119700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.539999999999948 " " y[1] (analytic) = 2.892887798126639 " " y[1] (numeric) = 2.892887798126668 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9781950267642020000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.3145454545454 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.549999999999947 " " y[1] (analytic) = 2.8983013631506456 " " y[1] (numeric) = 2.8983013631506744 " " absolute error = 2.88657986402540700000000000000E-14 " " relative error = 9.9595573487482450000000000000E-13 "%" Correct digits = 16 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.324999999999946 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.646158015252499 " " Order of pole (six term test) = 1.939781668625073500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.559999999999947 " " y[1] (analytic) = 2.9037142451602636 " " y[1] (numeric) = 2.903714245160293 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0093929834506303000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.335454545454493 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.569999999999947 " " y[1] (analytic) = 2.9091264464078095 " " y[1] (numeric) = 2.909126446407839 " " absolute error = 2.93098878501041300000000000000E-14 " " relative error = 1.0075150870906968000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.345909090909037 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.579999999999947 " " y[1] (analytic) = 2.9145379691344764 " " y[1] (numeric) = 2.914537969134506 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0208814355844595000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.3563636363635805 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.589999999999947 " " y[1] (analytic) = 2.9199488155704088 " " y[1] (numeric) = 2.9199488155704385 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0189896789044156000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.366818181818127 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.599999999999946 " " y[1] (analytic) = 2.9253589879347737 " " y[1] (numeric) = 2.9253589879348034 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0171051547064902000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.377272727272671 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.609999999999946 " " y[1] (analytic) = 2.930768488435833 " " y[1] (numeric) = 2.930768488435863 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0152278208721308000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.3877272727272185 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.619999999999946 " " y[1] (analytic) = 2.9361773192710157 " " y[1] (numeric) = 2.9361773192710454 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.013357635612464000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.398181818181762 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.629999999999946 " " y[1] (analytic) = 2.941585482626987 " " y[1] (numeric) = 2.941585482627017 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 1.0114945574650566000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.408636363636307 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.6399999999999455 " " y[1] (analytic) = 2.9469929806797195 " " y[1] (numeric) = 2.9469929806797497 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0247077773099791000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.419090909090852 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.649999999999945 " " y[1] (analytic) = 2.952399815594563 " " y[1] (numeric) = 2.9523998155945934 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0228311934683847000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.429545454545398 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.659999999999945 " " y[1] (analytic) = 2.957805989526314 " " y[1] (numeric) = 2.957805989526344 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0209616985271036000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.439999999999943 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.669999999999945 " " y[1] (analytic) = 2.963211504619281 " " y[1] (numeric) = 2.963211504619311 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.019099251698004100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.450454545454490 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.679999999999945 " " y[1] (analytic) = 2.9686163630073565 " " y[1] (numeric) = 2.9686163630073867 " " absolute error = 3.01980662698042600000000000000E-14 " " relative error = 1.0172438125084006000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.460909090909034 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.689999999999944 " " y[1] (analytic) = 2.9740205668140822 " " y[1] (numeric) = 2.974020566814113 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0303276252214931000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.47136363636358 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.699999999999944 " " y[1] (analytic) = 2.9794241181527177 " " y[1] (numeric) = 2.9794241181527483 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0284589996087184000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.481818181818124 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.115712895772642 " " Order of pole (six term test) = 3.06190628407421200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.709999999999944 " " y[1] (analytic) = 2.984827019126303 " " y[1] (numeric) = 2.9848270191263335 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0265973633749695000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.4922727272726695 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.719999999999944 " " y[1] (analytic) = 2.990229271827728 " " y[1] (numeric) = 2.9902292718277588 " " absolute error = 3.06421554796543200000000000000E-14 " " relative error = 1.0247426767020046000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.502727272727215 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 6.806927752970446 " " Order of pole (six term test) = 2.053113234978809500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.729999999999944 " " y[1] (analytic) = 2.9956308783397962 " " y[1] (numeric) = 2.9956308783398273 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 1.0377194638457138000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.51318181818176 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.739999999999943 " " y[1] (analytic) = 3.0010318407352896 " " y[1] (numeric) = 3.001031840735321 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.0506497622374152000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.523636363636305 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.801899262784033 " " Order of pole (six term test) = 4.938627284900576300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.749999999999943 " " y[1] (analytic) = 3.0064321610770333 " " y[1] (numeric) = 3.006432161077065 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.048762526810481000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.53409090909085 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.759999999999943 " " y[1] (analytic) = 3.0118318414179575 " " y[1] (numeric) = 3.011831841417989 " " absolute error = 3.153033389935444600000000000000E-14 " " relative error = 1.046882281598766000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.544545454545395 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.769999999999943 " " y[1] (analytic) = 3.0172308838011626 " " y[1] (numeric) = 3.0172308838011945 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0597274236077867000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.554999999999941 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.7799999999999425 " " y[1] (analytic) = 3.022629290259982 " " y[1] (numeric) = 3.022629290260014 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0578347537436299000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.565454545454484 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.789999999999942 " " y[1] (analytic) = 3.0280270628180426 " " y[1] (numeric) = 3.0280270628180745 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0559490534885581000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.575909090909030 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.799999999999942 " " y[1] (analytic) = 3.033424203489327 " " y[1] (numeric) = 3.033424203489359 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0540702837547268000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.586363636363577 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.809999999999942 " " y[1] (analytic) = 3.0388207142782355 " " y[1] (numeric) = 3.0388207142782675 " " absolute error = 3.19744231092045100000000000000E-14 " " relative error = 1.0521984057489520000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.596818181818121 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.819999999999942 " " y[1] (analytic) = 3.044216597179646 " " y[1] (numeric) = 3.0442165971796786 " " absolute error = 3.24185123190545700000000000000E-14 " " relative error = 1.0649213445945048000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.607272727272667 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.8299999999999415 " " y[1] (analytic) = 3.049611854178976 " " y[1] (numeric) = 3.0496118541790085 " " absolute error = 3.24185123190545700000000000000E-14 " " relative error = 1.0630373263610743000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.617727272727211 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 24.929875584732876 " " Order of pole (six term test) = -2.2264856625042740000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.839999999999941 " " y[1] (analytic) = 3.0550064872522382 " " y[1] (numeric) = 3.055006487252271 " " absolute error = 3.286260152890463400000000000000E-14 " " relative error = 1.0756966201555342000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.628181818181758 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.849999999999941 " " y[1] (analytic) = 3.0604004983661044 " " y[1] (numeric) = 3.0604004983661377 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.0883115055214693000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.638636363636303 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.859999999999940 " " y[1] (analytic) = 3.065793889477962 " " y[1] (numeric) = 3.0657938894779955 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.086396931413615200000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.649090909090847 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.869999999999940 " " y[1] (analytic) = 3.0711866625359723 " " y[1] (numeric) = 3.0711866625360056 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 1.0844893000170933000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.659545454545394 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.87999999999994 " " y[1] (analytic) = 3.0765788194791286 " " y[1] (numeric) = 3.0765788194791623 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0970230872979499000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.669999999999938 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 8.643638481968779 " " Order of pole (six term test) = 1.082156586562632600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.88999999999994 " " y[1] (analytic) = 3.081970362237315 " " y[1] (numeric) = 3.0819703622373487 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0951039751110336000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.680454545454483 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.89999999999994 " " y[1] (analytic) = 3.0873612927313605 " " y[1] (numeric) = 3.0873612927313943 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0931917825123004000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.690909090909028 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90999999999994 " " y[1] (analytic) = 3.0927516128730987 " " y[1] (numeric) = 3.0927516128731325 " " absolute error = 3.37507799486047600000000000000E-14 " " relative error = 1.0912864715071968000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.701363636363574 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9199999999999395 " " y[1] (analytic) = 3.0981413245654212 " " y[1] (numeric) = 3.0981413245654554 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.1037220570708266000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.71181818181812 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.929999999999940 " " y[1] (analytic) = 3.1035304297023356 " " y[1] (numeric) = 3.10353042970237 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.101805506116287900000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.722272727272663 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.939999999999939 " " y[1] (analytic) = 3.108918930169019 " " y[1] (numeric) = 3.1089189301690534 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.0998958135134063000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.732727272727210 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.949999999999939 " " y[1] (analytic) = 3.1143068278418737 " " y[1] (numeric) = 3.114306827841908 " " absolute error = 3.41948691584548200000000000000E-14 " " relative error = 1.097992941888481100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.743181818181755 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.959999999999939 " " y[1] (analytic) = 3.1196941245885808 " " y[1] (numeric) = 3.1196941245886154 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1103318782213305000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.753636363636300 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.9699999999999385 " " y[1] (analytic) = 3.1250808222681554 " " y[1] (numeric) = 3.12508082226819 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1084180006315561000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.764090909090845 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.979999999999938 " " y[1] (analytic) = 3.130466922730999 " " y[1] (numeric) = 3.1304669227310336 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1065109206803593000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.77454545454539 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" "NO COMPLEX POLE (six term test) for Equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.989999999999938 " " y[1] (analytic) = 3.1358524278189526 " " y[1] (numeric) = 3.135852427818987 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.1046106016027343000000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.784999999999934 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 4.4561228112024995 " " Order of pole (six term test) = 2.44639863922202500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.999999999999938 " " y[1] (analytic) = 3.1412373393653508 " " y[1] (numeric) = 3.1412373393653854 " " absolute error = 3.463895836830488400000000000000E-14 " " relative error = 1.102717006900958100000000000E-12 "%" Correct digits = 15 h = 1.00E-2 " " "NO INFO (given) for Equation 1" Radius of convergence (ratio test) for eq 1 = 6.795454545454481 " " "Order 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 ) = (0.1 * x + 0.2) / (0.2 * x + 0.3);" Iterations = 491 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 56 Seconds "Time to Timeout "= 0 Years 0 Days 0 Hours 0 Minutes 0 Seconds Percent Done = 100.40816326530485 "%" (%o58) true (%o58) diffeq.max