(%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_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_x array_tmp1 , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 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_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial, 1, order_d + kkk) then (temporary : array_tmp9 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_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_x array_tmp1 , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 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_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if order_d + kkk < glob_max_terms then (if not subscript(array_y_set_initial, 1, order_d + kkk) then (temporary : array_tmp9 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) 1.0 (%i56) exact_soln_y(x) := block(---------) 1.0 + x x 1.0 (%o56) exact_soln_y(x) := block(---------) 1.0 + x 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/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), 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:50,"), omniout_str(ALWAYS, "/* # Not Given = 0 */"), omniout_str(ALWAYS, "/* # No Pole = 3 */"), omniout_str(ALWAYS, "/* # Pole = 4 */"), omniout_str(ALWAYS, "glob_type_given_pole:4,"), omniout_str(ALWAYS, "/* # Real Part */"), omniout_str(ALWAYS, "array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS, "/* # Imag Part */"), omniout_str(ALWAYS, "array_given_rad_poles[1,2]:1.0,"), omniout_str(ALWAYS, "/* # Order */"), omniout_str(ALWAYS, "array_given_ord_poles[1,1]:1.0,"), omniout_str(ALWAYS, "/* # Not Used */"), omniout_str(ALWAYS, "array_given_ord_poles[1,2]:0.0,"), omniout_str(ALWAYS, ""), 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, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+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_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 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_tmp7 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp9 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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), iiif, jjjf x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 50, glob_type_given_pole : 4, array_given_rad_poles : 0.0, array_given_rad_poles : 1.0, 1, 1 1, 2 array_given_ord_poles : 1.0, array_given_ord_poles : 0.0, 1, 1 1, 2 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 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "2013-05-26T04:44:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), 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:50,"), omniout_str(ALWAYS, "/* # Not Given = 0 */"), omniout_str(ALWAYS, "/* # No Pole = 3 */"), omniout_str(ALWAYS, "/* # Pole = 4 */"), omniout_str(ALWAYS, "glob_type_given_pole:4,"), omniout_str(ALWAYS, "/* # Real Part */"), omniout_str(ALWAYS, "array_given_rad_poles[1,1]:0.0,"), omniout_str(ALWAYS, "/* # Imag Part */"), omniout_str(ALWAYS, "array_given_rad_poles[1,2]:1.0,"), omniout_str(ALWAYS, "/* # Order */"), omniout_str(ALWAYS, "array_given_ord_poles[1,1]:1.0,"), omniout_str(ALWAYS, "/* # Not Used */"), omniout_str(ALWAYS, "array_given_ord_poles[1,2]:0.0,"), omniout_str(ALWAYS, ""), 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, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 0.0, glob_smallish_float : 0.0, glob_large_float : 1.0E+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_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 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_tmp7 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp9 : 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, 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), iiif, jjjf x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 50, glob_type_given_pole : 4, array_given_rad_poles : 0.0, array_given_rad_poles : 1.0, 1, 1 1, 2 array_given_ord_poles : 1.0, array_given_ord_poles : 0.0, 1, 1 1, 2 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 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "2013-05-26T04:44:18-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 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/sing4postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:50," "/* # Not Given = 0 */" "/* # No Pole = 3 */" "/* # Pole = 4 */" "glob_type_given_pole:4," "/* # Real Part */" "array_given_rad_poles[1,1]:0.0," "/* # Imag Part */" "array_given_rad_poles[1,2]:1.0," "/* # Order */" "array_given_ord_poles[1,1]:1.0," "/* # Not Used */" "array_given_ord_poles[1,2]:0.0," "" "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.01," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0 / (x * x + 1.0)) " "));" "" "" "/* 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 = 3. "" estimated_steps = 3000000. "" step_error = 3.333333333333333700000000000000000E-17 "" est_needed_step_err = 3.333333333333333700000000000000000E-17 "" opt_iter = 1 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.753634911894619600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" estimated_step_error = 1.753634911894619600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-167 "" 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 = 1.1768422476818488000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 "" estimated_step_error = 1.1768422476818488000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-159 "" 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 = 7.89762483319751600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" estimated_step_error = 7.89762483319751600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-152 "" 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 = 5.299966309252228000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" estimated_step_error = 5.299966309252228000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-144 "" 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 = 3.55669349611086260000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" estimated_step_error = 3.55669349611086260000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-136 "" 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 = 2.38678454378318200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" estimated_step_error = 2.38678454378318200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-128 "" best_h = 6.400000E-5 "" opt_iter = 7 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.6016472776503507000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" estimated_step_error = 1.6016472776503507000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-120 "" 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 = 1.07471747824038450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 "" estimated_step_error = 1.07471747824038450000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-112 "" 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 = 7.210564417420875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" estimated_step_error = 7.210564417420875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" 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 = 4.8365887535279830000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" estimated_step_error = 4.8365887535279830000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-97 "" 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 = 3.24263923383055800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" estimated_step_error = 3.24263923383055800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" 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 = 2.171880439137025300000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" estimated_step_error = 2.171880439137025300000000000000000000000000000000000000000000000000000000000000000000000000000000E-81 "" best_h = 4.096000E-3 "" opt_iter = 13 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.45185569375015750000000000000000000000000000000000000000000000000000000000000000000000000E-73 "" estimated_step_error = 1.45185569375015750000000000000000000000000000000000000000000000000000000000000000000000000E-73 "" 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 = 9.666957169645851000000000000000000000000000000000000000000000000000000000000000000E-66 "" estimated_step_error = 9.666957169645851000000000000000000000000000000000000000000000000000000000000000000E-66 "" 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 = 6.3844681200201560000000000000000000000000000000000000000000000000000000000E-58 "" estimated_step_error = 6.3844681200201560000000000000000000000000000000000000000000000000000000000E-58 "" 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 = 4.14497829526225200000000000000000000000000000000000000000000000000E-50 "" estimated_step_error = 4.14497829526225200000000000000000000000000000000000000000000000000E-50 "" best_h = 6.553600E-2 "" opt_iter = 17 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 2.590479623172475000000000000000000000000000000000000000000E-42 "" estimated_step_error = 2.590479623172475000000000000000000000000000000000000000000E-42 "" best_h = 0.131072 "" opt_iter = 18 hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_estimated_step_error = 1.47153505203275470000000000000000000000000000000000E-34 "" estimated_step_error = 1.47153505203275470000000000000000000000000000000000E-34 "" best_h = 0.1 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -2. " " y[1] (analytic) = 0.2 " " y[1] (numeric) = 0.2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.23606797749979 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.2360679774998107 " " Order of pole (six term test) = 1.0000000000002576 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.99 " " y[1] (analytic) = 0.2016088385314812 " " y[1] (numeric) = 0.20160883853148123 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.376704306110809700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2271281956816047 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.107470135050775000E-3 " " Order of pole (three term test) = -0.8974866636184888 " " Radius of convergence (six term test) for eq 1 = 2.2271281956814093 " " Order of pole (six term test) = 0.9999999999976268 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.98 " " y[1] (analytic) = 0.20323550930818632 " " y[1] (numeric) = 0.20323550930818635 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.365685342591405000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2181974664127626 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.403966542792352000E-3 " " Order of pole (three term test) = -1.3186640511580892 " " Radius of convergence (six term test) for eq 1 = 2.2181974664126605 " " Order of pole (six term test) = 0.9999999999987601 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.97 " " y[1] (analytic) = 0.20488024749533895 " " y[1] (numeric) = 0.204880247495339 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.709443780446463300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2092758994747577 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.548327623996661700E-2 " " Order of pole (three term test) = -2.420779408031582 " " Radius of convergence (six term test) for eq 1 = 2.2092758994747785 " " Order of pole (six term test) = 1.0000000000002416 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.96 " " y[1] (analytic) = 0.20654329147389294 " " y[1] (numeric) = 0.20654329147389297 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.343813949006289500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.2003636063160106 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.930926230785463800E-2 " " Order of pole (three term test) = -4.197173604726942 " " Radius of convergence (six term test) for eq 1 = 2.2003636063159635 " " Order of pole (six term test) = 0.999999999999428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.95 " " y[1] (analytic) = 0.20822488287350338 " " y[1] (numeric) = 0.20822488287350344 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.66592303788115700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.191460700081113 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.08569904875259700E-2 " " Order of pole (three term test) = -6.636477211794843 " " Radius of convergence (six term test) for eq 1 = 2.191460700081046 " " Order of pole (six term test) = 0.9999999999992006 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.94 " " y[1] (analytic) = 0.2099252666050886 " " y[1] (numeric) = 0.20992526660508865 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.64432920005219800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.182567295640618 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.011422571928080400E-2 " " Order of pole (three term test) = -9.722016327564818 " " Radius of convergence (six term test) for eq 1 = 2.182567295640572 " " Order of pole (six term test) = 0.9999999999994511 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.93 " " y[1] (analytic) = 0.21164469089292895 " " y[1] (numeric) = 0.211644690892929 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.62284638452570100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1736835096213984 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.70833253584714520E-2 " " Order of pole (three term test) = -13.431122740504458 " " Radius of convergence (six term test) for eq 1 = 2.17368350962136 " " Order of pole (six term test) = 0.9999999999995399 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.92 " " y[1] (analytic) = 0.21338340730624786 " " y[1] (numeric) = 0.2133834073062479 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.60147459130166700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1648094604375694 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.178352850738162600E-2 " " Order of pole (three term test) = -17.734361553929336 " " Radius of convergence (six term test) for eq 1 = 2.1648094604373664 " " Order of pole (six term test) = 0.9999999999975486 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.91 " " y[1] (analytic) = 0.21514167079021537 " " y[1] (numeric) = 0.2151416707902154 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.290106910190047300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1559452683219953 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.2536211154803866000E-3 " " Order of pole (three term test) = -22.594697827612297 " " Radius of convergence (six term test) for eq 1 = 2.1559452683219775 " " Order of pole (six term test) = 0.9999999999997904 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9 " " y[1] (analytic) = 0.2169197396963124 " " y[1] (numeric) = 0.2169197396963124 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1470910553583886 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.147091055358213 " " Order of pole (six term test) = 0.999999999997879 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.89 " " y[1] (analytic) = 0.21871787581199012 " " y[1] (numeric) = 0.21871787581199015 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.269012672722169600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1382469455140116 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.9090219001654879 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1382469455143296 " " Order of pole (six term test) = 1.000000000003844 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.88 " " y[1] (analytic) = 0.2205363443895554 " " y[1] (numeric) = 0.22053634438955544 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.258548820715077500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1294130646729865 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.8403326031302475 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.129413064672895 " " Order of pole (six term test) = 0.9999999999989022 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8699999999999999 " " y[1] (analytic) = 0.2223754141742089 " " y[1] (numeric) = 0.22237541417420895 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.496280959718433200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1205895406702355 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.1205895406702773 " " Order of pole (six term test) = 1.0000000000005045 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8599999999999999 " " y[1] (analytic) = 0.22423535743115974 " " y[1] (numeric) = 0.2242353574311598 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.47557530030917400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1117765033260505 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.111776503326158 " " Order of pole (six term test) = 1.0000000000013003 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8499999999999999 " " y[1] (analytic) = 0.22611644997173547 " " y[1] (numeric) = 0.2261164499717355 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.227490331601188600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.1029740844813087 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.102974084481246 " " Order of pole (six term test) = 0.9999999999992415 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8399999999999999 " " y[1] (analytic) = 0.22801897117840209 " " y[1] (numeric) = 0.22801897117840209 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.094182418033348 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0941824180333803 " " Order of pole (six term test) = 1.0000000000003944 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8299999999999998 " " y[1] (analytic) = 0.22994320402860496 " " y[1] (numeric) = 0.22994320402860496 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0854016399725017 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.085401639972721 " " Order of pole (six term test) = 1.000000000002645 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8199999999999998 " " y[1] (analytic) = 0.2318894351173361 " " y[1] (numeric) = 0.2318894351173361 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.076631888419322 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0766318884186017 " " Order of pole (six term test) = 0.9999999999913225 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8099999999999998 " " y[1] (analytic) = 0.2338579546783284 " " y[1] (numeric) = 0.23385795467832843 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.186856168899907800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.067873303662485 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0678733036625876 " " Order of pole (six term test) = 1.0000000000012363 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7999999999999998 " " y[1] (analytic) = 0.23584905660377362 " " y[1] (numeric) = 0.23584905660377364 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.176836406102665800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0591260281974 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0591260281973516 " " Order of pole (six term test) = 0.9999999999994156 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7899999999999998 " " y[1] (analytic) = 0.23786303846245335 " " y[1] (numeric) = 0.23786303846245338 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.16687215445665500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0503902067655315 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.7474366021634421 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0503902067655178 " " Order of pole (six term test) = 0.9999999999998366 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7799999999999998 " " y[1] (analytic) = 0.2399002015161693 " " y[1] (numeric) = 0.23990020151616934 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.156963413961875400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0416659863944444 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.8324802893165628 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0416659863942046 " " Order of pole (six term test) = 0.9999999999971099 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7699999999999998 " " y[1] (analytic) = 0.24196085073435122 " " y[1] (numeric) = 0.24196085073435125 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.147110184618327100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.032953516438583 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0329535164385524 " " Order of pole (six term test) = 0.9999999999996376 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7599999999999998 " " y[1] (analytic) = 0.24404529480671613 " " y[1] (numeric) = 0.2440452948067162 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.274624932852020700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0242529486207994 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0242529486207856 " " Order of pole (six term test) = 0.9999999999998295 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7499999999999998 " " y[1] (analytic) = 0.2461538461538462 " " y[1] (numeric) = 0.24615384615384622 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.127570259384924500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.0155644370746373 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0155644370745778 " " Order of pole (six term test) = 0.9999999999992859 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7399999999999998 " " y[1] (analytic) = 0.24828682093554477 " " y[1] (numeric) = 0.2482868209355448 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.1178835634950700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 2.006888138387389 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 2.0068881383874695 " " Order of pole (six term test) = 1.0000000000009663 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7299999999999998 " " y[1] (analytic) = 0.2504445390568259 " " y[1] (numeric) = 0.2504445390568259 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9982242116439284 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9982242116439097 " " Order of pole (six term test) = 0.9999999999997726 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7199999999999998 " " y[1] (analytic) = 0.25262732417138245 " " y[1] (numeric) = 0.2526273241713824 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.19735341033810900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.989572818471342 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9895728184713322 " " Order of pole (six term test) = 0.9999999999998828 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7099999999999997 " " y[1] (analytic) = 0.25483550368237307 " " y[1] (numeric) = 0.25483550368237307 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9809341230843591 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 1.2726518237591733 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9809341230843032 " " Order of pole (six term test) = 0.9999999999993339 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6999999999999997 " " y[1] (analytic) = 0.25706940874035994 " " y[1] (numeric) = 0.25706940874035994 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9723082923316018 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 1.3223488448361305 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9723082923315485 " " Order of pole (six term test) = 0.999999999999373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6899999999999997 " " y[1] (analytic) = 0.25932937423822 " " y[1] (numeric) = 0.25932937423822 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.963695495742657 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.963695495742691 " " Order of pole (six term test) = 1.0000000000003944 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6799999999999997 " " y[1] (analytic) = 0.26161573880284644 " " y[1] (numeric) = 0.26161573880284644 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9550959055759898 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9550959055760018 " " Order of pole (six term test) = 1.0000000000001332 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6699999999999997 " " y[1] (analytic) = 0.26392884478344647 " " y[1] (numeric) = 0.26392884478344647 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9465096968677036 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9465096968677196 " " Order of pole (six term test) = 1.0000000000001652 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6599999999999997 " " y[1] (analytic) = 0.266269038236234 " " y[1] (numeric) = 0.266269038236234 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9379370474811608 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9379370474811495 " " Order of pole (six term test) = 0.9999999999998401 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6499999999999997 " " y[1] (analytic) = 0.2686366689053057 " " y[1] (numeric) = 0.2686366689053057 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9293781381574735 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9293781381574682 " " Order of pole (six term test) = 0.9999999999999734 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6399999999999997 " " y[1] (analytic) = 0.27103209019947966 " " y[1] (numeric) = 0.2710320901994797 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.048139435828488200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.920833152566875 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9208331525668916 " " Order of pole (six term test) = 1.0000000000001545 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6299999999999997 " " y[1] (analytic) = 0.27345565916486647 " " y[1] (numeric) = 0.2734556591648665 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.02998728937586720000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9123022773609821 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.912302277360971 " " Order of pole (six term test) = 0.9999999999997993 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6199999999999997 " " y[1] (analytic) = 0.27590773645293026 " " y[1] (numeric) = 0.27590773645293026 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.9037857022259619 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.9037857022259617 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6099999999999997 " " y[1] (analytic) = 0.2783886862837895 " " y[1] (numeric) = 0.27838868628378954 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.99401606337801180000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8952836199366043 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8952836199366088 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5999999999999996 " " y[1] (analytic) = 0.28089887640449446 " " y[1] (numeric) = 0.2808988764044945 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.97619698383277800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8867962264113205 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8867962264113078 " " Order of pole (six term test) = 0.9999999999997673 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5899999999999996 " " y[1] (analytic) = 0.2834386780420057 " " y[1] (numeric) = 0.28343867804200573 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.95848892659000700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8783237207680679 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8783237207680754 " " Order of pole (six term test) = 1.000000000000112 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5799999999999996 " " y[1] (analytic) = 0.2860084658505893 " " y[1] (numeric) = 0.2860084658505893 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.869866305381216 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8698663053812257 " " Order of pole (six term test) = 1.0000000000001439 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5699999999999996 " " y[1] (analytic) = 0.2886086178533292 " " y[1] (numeric) = 0.28860861785332925 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.92340587901185200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8614241859393572 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8614241859393417 " " Order of pole (six term test) = 0.9999999999997602 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5599999999999996 " " y[1] (analytic) = 0.2912395153774465 " " y[1] (numeric) = 0.2912395153774466 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.90603088867646800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8529975715040747 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8529975715040772 " " Order of pole (six term test) = 1.000000000000048 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5499999999999996 " " y[1] (analytic) = 0.2939015429831007 " " y[1] (numeric) = 0.29390154298310084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.777533841287094600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8445866745696715 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.844586674569659 " " Order of pole (six term test) = 0.9999999999998153 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5399999999999996 " " y[1] (analytic) = 0.29659508838533644 " " y[1] (numeric) = 0.2965950883853365 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.871613974913088300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8361917111238681 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.836191711123883 " " Order of pole (six term test) = 1.000000000000231 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5299999999999996 " " y[1] (analytic) = 0.2993205423688229 " " y[1] (numeric) = 0.29932054236882294 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.85457205148509200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8278129007094788 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.8278129007094455 " " Order of pole (six term test) = 0.9999999999995026 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5199999999999996 " " y[1] (analytic) = 0.3020782986950219 " " y[1] (numeric) = 0.3020782986950219 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.819450466487065 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.08662346569851200000E-4 " " Order of pole (three term test) = -0.8937877954992438 " " Radius of convergence (six term test) for eq 1 = 1.819450466487062 " " Order of pole (six term test) = 0.9999999999999556 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.5099999999999996 " " y[1] (analytic) = 0.3048687540014025 " " y[1] (numeric) = 0.30486875400140256 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.820821271536487400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.811104635298579 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.677196947041653000E-3 " " Order of pole (three term test) = -1.4490910529692942 " " Radius of convergence (six term test) for eq 1 = 1.8111046352985798 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4999999999999996 " " y[1] (analytic) = 0.3076923076923078 " " y[1] (numeric) = 0.3076923076923079 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.804112415015878800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.8027756377319943 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.431932186432938200E-2 " " Order of pole (three term test) = -3.0180183118199295 " " Radius of convergence (six term test) for eq 1 = 1.8027756377319202 " " Order of pole (six term test) = 0.999999999998904 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4899999999999995 " " y[1] (analytic) = 0.3105493618210616 " " y[1] (numeric) = 0.31054936182106163 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.787514580797732700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.794463708186933 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.723112030880121800E-2 " " Order of pole (three term test) = -5.571567493936945 " " Radius of convergence (six term test) for eq 1 = 1.7944637081868788 " " Order of pole (six term test) = 0.9999999999992006 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4799999999999995 " " y[1] (analytic) = 0.3134403209628888 " " y[1] (numeric) = 0.3134403209628888 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7861690849412881 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.735294265228638800E-2 " " Order of pole (three term test) = -9.059862761054964 " " Radius of convergence (six term test) for eq 1 = 1.7861690849411944 " " Order of pole (six term test) = 0.9999999999986144 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4699999999999995 " " y[1] (analytic) = 0.31636559207820575 " " y[1] (numeric) = 0.31636559207820575 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.777892010218843 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.467563877808635300E-2 " " Order of pole (three term test) = -13.410175452670337 " " Radius of convergence (six term test) for eq 1 = 1.7778920102188016 " " Order of pole (six term test) = 0.9999999999993907 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4599999999999995 " " y[1] (analytic) = 0.31932558436581954 " " y[1] (numeric) = 0.3193255843658196 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.738387211958069300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7696327302578911 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.247938082717088000E-3 " " Order of pole (three term test) = -18.524927077512558 " " Radius of convergence (six term test) for eq 1 = 1.7696327302578416 " " Order of pole (six term test) = 0.9999999999992717 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4499999999999995 " " y[1] (analytic) = 0.32232070910556015 " " y[1] (numeric) = 0.3223207091055602 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.722233466949773500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7613914953808534 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1845813796640103000E-3 " " Order of pole (three term test) = -24.27996276827301 " " Radius of convergence (six term test) for eq 1 = 1.7613914953820253 " " Order of pole (six term test) = 1.0000000000173106 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4399999999999995 " " y[1] (analytic) = 0.3253513794898492 " " y[1] (numeric) = 0.3253513794898492 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7531685600648896 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7531685600649078 " " Order of pole (six term test) = 1.0000000000002682 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4299999999999995 " " y[1] (analytic) = 0.3284180104436929 " " y[1] (numeric) = 0.3284180104436929 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7449641830135076 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7449641830135392 " " Order of pole (six term test) = 1.0000000000004636 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4199999999999995 " " y[1] (analytic) = 0.33152101843256876 " " y[1] (numeric) = 0.3315210184325688 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.674438365739660300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.736778627229158 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7367786272291201 " " Order of pole (six term test) = 0.9999999999994404 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.4099999999999995 " " y[1] (analytic) = 0.33466082125765556 " " y[1] (numeric) = 0.33466082125765556 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7286121600868132 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7286121600867779 " " Order of pole (six term test) = 0.9999999999994831 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3999999999999995 " " y[1] (analytic) = 0.33783783783783805 " " y[1] (numeric) = 0.33783783783783805 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7204650534085248 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7204650534084667 " " Order of pole (six term test) = 0.9999999999991473 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3899999999999995 " " y[1] (analytic) = 0.3410524879779 " " y[1] (numeric) = 0.3410524879779 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7123375835389465 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7123375835389771 " " Order of pole (six term test) = 1.0000000000004512 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3799999999999994 " " y[1] (analytic) = 0.3443051921222974 " " y[1] (numeric) = 0.34430519212229743 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.612265876360651500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.7042300314218144 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.7042300314216277 " " Order of pole (six term test) = 0.9999999999972573 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3699999999999994 " " y[1] (analytic) = 0.34759637109388597 " " y[1] (numeric) = 0.347596371093886 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.597000309772055600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6961426826773738 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6961426826774377 " " Order of pole (six term test) = 1.000000000000938 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3599999999999994 " " y[1] (analytic) = 0.350926445816957 " " y[1] (numeric) = 0.35092644581695703 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.58184576548592200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.688075827680735 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6880758276807395 " " Order of pole (six term test) = 1.0000000000000675 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3499999999999994 " " y[1] (analytic) = 0.35429583702391515 " " y[1] (numeric) = 0.35429583702391526 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.133604487004502700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6800297616411437 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6800297616411586 " " Order of pole (six term test) = 1.0000000000002185 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3399999999999994 " " y[1] (analytic) = 0.3577049649449136 " " y[1] (numeric) = 0.3577049649449137 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.103739487642086500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6720047846821486 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.672004784682114 " " Order of pole (six term test) = 0.9999999999994884 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3299999999999994 " " y[1] (analytic) = 0.3611542489797394 " " y[1] (numeric) = 0.3611542489797395 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.074096532884594300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6640012019226424 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6640012019226416 " " Order of pole (six term test) = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3199999999999994 " " y[1] (analytic) = 0.36464410735122543 " " y[1] (numeric) = 0.3646441073512255 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.522337811366013800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6560193235587555 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.656019323558717 " " Order of pole (six term test) = 0.9999999999994351 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.3099999999999994 " " y[1] (analytic) = 0.36817495673944284 " " y[1] (numeric) = 0.3681749567394429 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.507738378592192700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6480594649465772 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6480594649465645 " " Order of pole (six term test) = 0.9999999999998099 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2999999999999994 " " y[1] (analytic) = 0.371747211895911 " " y[1] (numeric) = 0.3717472118959111 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.98649993624166940000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.640121946685672 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6401219466856858 " " Order of pole (six term test) = 1.0000000000002007 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2899999999999994 " " y[1] (analytic) = 0.3753612852370409 " " y[1] (numeric) = 0.375361285237041 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.95774515990387800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6322070947033647 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6322070947033525 " " Order of pole (six term test) = 0.9999999999998188 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2799999999999994 " " y[1] (analytic) = 0.37901758641600997 " " y[1] (numeric) = 0.37901758641601 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.464606214085505400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6243152403397556 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6243152403397394 " " Order of pole (six term test) = 0.9999999999997744 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2699999999999994 " " y[1] (analytic) = 0.38271652187224947 " " y[1] (numeric) = 0.3827165218722495 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.45045087052153500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.616446720433432 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6164467204334256 " " Order of pole (six term test) = 0.9999999999999094 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2599999999999993 " " y[1] (analytic) = 0.38645849435770624 " " y[1] (numeric) = 0.3864584943577063 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.436406549260026400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.608601877407831 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.6086018774078337 " " Order of pole (six term test) = 1.0000000000000409 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2499999999999993 " " y[1] (analytic) = 0.3902439024390247 " " y[1] (numeric) = 0.3902439024390247 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.6007810593582117 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.600781059358218 " " Order of pole (six term test) = 1.0000000000000693 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2399999999999993 " " y[1] (analytic) = 0.39407313997477955 " " y[1] (numeric) = 0.3940731399747796 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.408650973644397800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5929846201391897 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5929846201391875 " " Order of pole (six term test) = 0.9999999999999769 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2299999999999993 " " y[1] (analytic) = 0.39794659556687517 " " y[1] (numeric) = 0.3979465955668752 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.394939719290277000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5852129194527775 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.585212919452769 " " Order of pole (six term test) = 0.9999999999998366 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2199999999999993 " " y[1] (analytic) = 0.4018646519852116 " " y[1] (numeric) = 0.4018646519852117 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.76267897447723800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5774663229368793 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.577466322936858 " " Order of pole (six term test) = 0.9999999999995985 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.2099999999999993 " " y[1] (analytic) = 0.4058276855647095 " " y[1] (numeric) = 0.40582768556470955 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.367850277489423300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5697452022541742 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5697452022541665 " " Order of pole (six term test) = 0.9999999999998685 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1999999999999993 " " y[1] (analytic) = 0.4098360655737707 " " y[1] (numeric) = 0.40983606557377084 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.708944180085380300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5620499351813304 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.5620499351813584 " " Order of pole (six term test) = 1.0000000000004885 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1899999999999993 " " y[1] (analytic) = 0.41389015355324726 " " y[1] (numeric) = 0.4138901535532473 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.341204924898419200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5543809056984708 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6497677320741136000E-3 " " Order of pole (three term test) = -0.9144195410382225 " " Radius of convergence (six term test) for eq 1 = 1.5543809056984688 " " Order of pole (six term test) = 0.9999999999999645 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1799999999999993 " " y[1] (analytic) = 0.4179903026249794 " " y[1] (numeric) = 0.41799030262497944 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.328048782056611400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5467385040788242 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.408640985014106000E-3 " " Order of pole (three term test) = -1.8574593049414083 " " Radius of convergence (six term test) for eq 1 = 1.5467385040788353 " " Order of pole (six term test) = 1.0000000000001918 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1699999999999993 " " y[1] (analytic) = 0.42213685676896484 " " y[1] (numeric) = 0.42213685676896484 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5391231269784749 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.416363850984418000E-2 " " Order of pole (three term test) = -4.1617351448615745 " " Radius of convergence (six term test) for eq 1 = 1.5391231269784462 " " Order of pole (six term test) = 0.9999999999995097 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1599999999999993 " " y[1] (analytic) = 0.4263301500682131 " " y[1] (numeric) = 0.4263301500682132 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.302069563280382800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5315351775261312 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.572316436464573600E-2 " " Order of pole (three term test) = -7.735128418293754 " " Radius of convergence (six term test) for eq 1 = 1.531535177526099 " " Order of pole (six term test) = 0.9999999999994458 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1499999999999992 " " y[1] (analytic) = 0.43057050592034485 " " y[1] (numeric) = 0.4305705059203448 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.28924648734596200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5239750654128164 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.40119311408490200E-2 " " Order of pole (three term test) = -12.425927607287806 " " Radius of convergence (six term test) for eq 1 = 1.523975065412798 " " Order of pole (six term test) = 0.9999999999996838 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1399999999999992 " " y[1] (analytic) = 0.43485823621499425 " " y[1] (numeric) = 0.43485823621499425 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5164432069813885 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.089348792332215000E-3 " " Order of pole (three term test) = -18.020255207085082 " " Radius of convergence (six term test) for eq 1 = 1.5164432069813703 " " Order of pole (six term test) = 0.9999999999996909 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1299999999999992 " " y[1] (analytic) = 0.4391936404760863 " " y[1] (numeric) = 0.4391936404760863 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5089400253157839 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.1679326961019973000E-3 " " Order of pole (three term test) = -24.242024218514192 " " Radius of convergence (six term test) for eq 1 = 1.5089400253156138 " " Order of pole (six term test) = 0.9999999999970708 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1199999999999992 " " y[1] (analytic) = 0.4435770049680628 " " y[1] (numeric) = 0.44357700496806285 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.251443393357475600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.5014659503298762 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.501465950329905 " " Order of pole (six term test) = 1.0000000000004992 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.1099999999999992 " " y[1] (analytic) = 0.4480086017651543 " " y[1] (numeric) = 0.4480086017651543 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4940214188558336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4940214188558685 " " Order of pole (six term test) = 1.0000000000006022 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0999999999999992 " " y[1] (analytic) = 0.4524886877828058 " " y[1] (numeric) = 0.4524886877828058 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.48660687473185 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4866068747318344 " " Order of pole (six term test) = 0.9999999999997335 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0899999999999992 " " y[1] (analytic) = 0.4570175037703948 " " y[1] (numeric) = 0.4570175037703948 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.479222768889121 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4792227688891162 " " Order of pole (six term test) = 0.9999999999999183 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0799999999999992 " " y[1] (analytic) = 0.4615952732644021 " " y[1] (numeric) = 0.46159527326440214 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.202593580273968700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4718695594379274 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4718695594379114 " " Order of pole (six term test) = 0.9999999999997264 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0699999999999992 " " y[1] (analytic) = 0.46622220150123594 " " y[1] (numeric) = 0.46622220150123583 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.381317365518495800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4645477117526755 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4645477117527312 " " Order of pole (six term test) = 1.000000000000961 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0599999999999992 " " y[1] (analytic) = 0.47089847428894377 " " y[1] (numeric) = 0.47089847428894366 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.3576696150939800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4572576985557488 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4572576985557555 " " Order of pole (six term test) = 1.000000000000119 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0499999999999992 " " y[1] (analytic) = 0.4756242568370991 " " y[1] (numeric) = 0.4756242568370991 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4499999999999993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4499999999999924 " " Order of pole (six term test) = 0.9999999999998828 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0399999999999991 " " y[1] (analytic) = 0.48039969254419723 " " y[1] (numeric) = 0.4803996925441972 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.155520124029861800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.442775103749714 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.44277510374969 " " Order of pole (six term test) = 0.999999999999595 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0299999999999991 " " y[1] (analytic) = 0.48522490174195776 " " y[1] (numeric) = 0.4852249017419578 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.144029315724991600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4355835050598758 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4355835050598993 " " Order of pole (six term test) = 1.0000000000004015 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0199999999999991 " " y[1] (analytic) = 0.4900999803960012 " " y[1] (numeric) = 0.4900999803960012 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4284257068535269 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4284257068535196 " " Order of pole (six term test) = 0.9999999999998739 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.0099999999999991 " " y[1] (analytic) = 0.4950249987624379 " " y[1] (numeric) = 0.49502499876243794 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.121380766022638500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4213022197970417 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.421302219797042 " " Order of pole (six term test) = 1.0000000000000053 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9999999999999991 " " y[1] (analytic) = 0.5000000000000004 " " y[1] (numeric) = 0.5000000000000004 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4142135623730945 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4142135623730983 " " Order of pole (six term test) = 1.00062342576914 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9899999999999991 " " y[1] (analytic) = 0.505024998737438 " " y[1] (numeric) = 0.505024998737438 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4071602609511107 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.4071602609511025 " " Order of pole (six term test) = 0.9999999999998597 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9799999999999991 " " y[1] (analytic) = 0.5100999795960013 " " y[1] (numeric) = 0.5100999795960013 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.4001428498549704 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.400142849854974 " " Order of pole (six term test) = 1.0000000000000497 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9699999999999991 " " y[1] (analytic) = 0.5152248956669591 " " y[1] (numeric) = 0.5152248956669591 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.393161871427724 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.393161871427725 " " Order of pole (six term test) = 1.0000000000000195 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9599999999999991 " " y[1] (analytic) = 0.5203996669442137 " " y[1] (numeric) = 0.5203996669442136 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.133404564119698600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.386217876093076 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.386217876093077 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9499999999999991 " " y[1] (analytic) = 0.5256241787122213 " " y[1] (numeric) = 0.5256241787122212 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.11219930434935800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3793114224133716 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3793114224133691 " " Order of pole (six term test) = 0.9999999999999556 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.9399999999999991 " " y[1] (analytic) = 0.5308982798895737 " " y[1] (numeric) = 0.5308982798895736 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.091216089183942400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3724430771438203 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.1633603647915315000E-3 " " Order of pole (three term test) = -0.9997516172657827 " " Radius of convergence (six term test) for eq 1 = 1.372443077143823 " " Order of pole (six term test) = 1.0000000000000586 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.929999999999999 " " y[1] (analytic) = 0.5362217813287581 " " y[1] (numeric) = 0.5362217813287581 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.36561341528267 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.03014134345769800E-2 " " Order of pole (three term test) = -2.501448188445504 " " Radius of convergence (six term test) for eq 1 = 1.3656134152826698 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.919999999999999 " " y[1] (analytic) = 0.5415944540727908 " " y[1] (numeric) = 0.5415944540727908 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3588230201170417 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.40738993522449800E-2 " " Order of pole (three term test) = -5.680269755514649 " " Radius of convergence (six term test) for eq 1 = 1.3588230201170308 " " Order of pole (six term test) = 0.9999999999997922 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.909999999999999 " " y[1] (analytic) = 0.5470160275696083 " " y[1] (numeric) = 0.5470160275696083 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3520724832641178 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.420578503033822200E-2 " " Order of pole (three term test) = -10.309797357988511 " " Radius of convergence (six term test) for eq 1 = 1.3520724832641147 " " Order of pole (six term test) = 0.9999999999999378 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.899999999999999 " " y[1] (analytic) = 0.5524861878453043 " " y[1] (numeric) = 0.5524861878453045 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 2.009503674571531700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3453624047073705 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.066553089629887600E-2 " " Order of pole (three term test) = -16.037779759885606 " " Radius of convergence (six term test) for eq 1 = 1.3453624047073505 " " Order of pole (six term test) = 0.9999999999996163 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.889999999999999 " " y[1] (analytic) = 0.5580045756375208 " " y[1] (numeric) = 0.5580045756375208 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3386933928274982 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.703204801790985000E-3 " " Order of pole (three term test) = -22.393585924061796 " " Radius of convergence (six term test) for eq 1 = 1.3386933928274871 " " Order of pole (six term test) = 0.9999999999997868 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.879999999999999 " " y[1] (analytic) = 0.5635707844905326 " " y[1] (numeric) = 0.5635707844905326 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3320660644277362 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3320660644277238 " " Order of pole (six term test) = 0.9999999999997513 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.869999999999999 " " y[1] (analytic) = 0.5691843588138205 " " y[1] (numeric) = 0.5691843588138203 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.950550831963935300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3254810447531862 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3254810447531866 " " Order of pole (six term test) = 1.000000000000007 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.859999999999999 " " y[1] (analytic) = 0.5748447919061859 " " y[1] (numeric) = 0.5748447919061859 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3189389675038032 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3189389675037613 " " Order of pole (six term test) = 0.9999999999991864 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.849999999999999 " " y[1] (analytic) = 0.5805515239477509 " " y[1] (numeric) = 0.5805515239477509 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3124404748406682 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.312440474840654 " " Order of pole (six term test) = 0.99999999999973 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.839999999999999 " " y[1] (analytic) = 0.5863039399624772 " " y[1] (numeric) = 0.5863039399624771 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.893596390800664800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.30598621738516 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.3059862173851662 " " Order of pole (six term test) = 1.000000000000119 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.829999999999999 " " y[1] (analytic) = 0.5921013677541601 " " y[1] (numeric) = 0.5921013677541601 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2995768542106305 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2995768542107098 " " Order of pole (six term test) = 1.0000000000015294 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.819999999999999 " " y[1] (analytic) = 0.5979430758191826 " " y[1] (numeric) = 0.5979430758191826 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2932130528261763 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.293213052826167 " " Order of pole (six term test) = 0.9999999999998188 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.8099999999999989 " " y[1] (analytic) = 0.6038282712396601 " " y[1] (numeric) = 0.60382827123966 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.838640351081719800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2868954891520905 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2868954891520892 " " Order of pole (six term test) = 0.9999999999999734 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7999999999999989 " " y[1] (analytic) = 0.6097560975609763 " " y[1] (numeric) = 0.6097560975609762 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.820765760385254800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2806248474865691 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.280624847486576 " " Order of pole (six term test) = 1.0000000000001315 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7899999999999989 " " y[1] (analytic) = 0.6157256326580882 " " y[1] (numeric) = 0.6157256326580881 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.803113214293714800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2744018204632315 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2744018204632293 " " Order of pole (six term test) = 0.9999999999999591 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7799999999999989 " " y[1] (analytic) = 0.6217358865953749 " " y[1] (numeric) = 0.6217358865953748 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.785682712807099800000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2682271089990145 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2682271089990147 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7699999999999989 " " y[1] (analytic) = 0.6277857994852163 " " y[1] (numeric) = 0.6277857994852162 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.768474255925410200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2621014222319846 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.262101422231983 " " Order of pole (six term test) = 0.9999999999999662 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7599999999999989 " " y[1] (analytic) = 0.6338742393509135 " " y[1] (numeric) = 0.6338742393509134 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.75148784364864500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.256025477448606 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2560254774486073 " " Order of pole (six term test) = 1.0000000000000249 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7499999999999989 " " y[1] (analytic) = 0.6400000000000007 " " y[1] (numeric) = 0.6400000000000006 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.734723475976805200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2499999999999993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2499999999999976 " " Order of pole (six term test) = 0.9999999999999609 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7399999999999989 " " y[1] (analytic) = 0.6461617989144489 " " y[1] (numeric) = 0.6461617989144488 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.718181152909890300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2440257232067182 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.039999612215102000E-3 " " Order of pole (three term test) = -1.1109196667412213 " " Radius of convergence (six term test) for eq 1 = 1.2440257232067118 " " Order of pole (six term test) = 0.999999999999865 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7299999999999989 " " y[1] (analytic) = 0.6523582751647211 " " y[1] (numeric) = 0.6523582751647211 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2381033882515622 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.080499238455777300E-2 " " Order of pole (three term test) = -3.1394217643820803 " " Radius of convergence (six term test) for eq 1 = 1.238103388251559 " " Order of pole (six term test) = 0.999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7199999999999989 " " y[1] (analytic) = 0.6585879873551114 " " y[1] (numeric) = 0.6585879873551113 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.685762640590835700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2322337440599485 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.389496100298365500E-2 " " Order of pole (three term test) = -7.098427500344458 " " Radius of convergence (six term test) for eq 1 = 1.2322337440599425 " " Order of pole (six term test) = 0.9999999999998685 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.7099999999999989 " " y[1] (analytic) = 0.6648494116082714 " " y[1] (numeric) = 0.6648494116082714 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.226417547167358 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.295495946687287300E-2 " " Order of pole (three term test) = -12.550435708122736 " " Radius of convergence (six term test) for eq 1 = 1.2264175471673586 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6999999999999988 " " y[1] (analytic) = 0.6711409395973161 " " y[1] (numeric) = 0.6711409395973161 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2206555615733696 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.057311410353981000E-3 " " Order of pole (three term test) = -18.849683455055064 " " Radius of convergence (six term test) for eq 1 = 1.2206555615733559 " " Order of pole (six term test) = 0.9999999999997105 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6899999999999988 " " y[1] (analytic) = 0.677460876634375 " " y[1] (numeric) = 0.677460876634375 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.214948558581802 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2149485585819424 " " Order of pole (six term test) = 1.0000000000030038 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6799999999999988 " " y[1] (analytic) = 0.6838074398249461 " " y[1] (numeric) = 0.683807439824946 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.62359015121182730000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2092973166264773 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.209297316626482 " " Order of pole (six term test) = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6699999999999988 " " y[1] (analytic) = 0.690178756297882 " " y[1] (numeric) = 0.6901787562978818 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.608602140379387600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2037026210821336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.203702621082118 " " Order of pole (six term test) = 0.9999999999996749 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6599999999999988 " " y[1] (analytic) = 0.6965728615213159 " " y[1] (numeric) = 0.6965728615213158 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.59383617415187280000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.198165264060012 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1981652640600167 " " Order of pole (six term test) = 1.0000000000000924 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6499999999999988 " " y[1] (analytic) = 0.7029876977152907 " " y[1] (numeric) = 0.7029876977152907 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1926860441876557 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1926860441876626 " " Order of pole (six term test) = 1.0000000000001457 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6399999999999988 " " y[1] (analytic) = 0.709421112372305 " " y[1] (numeric) = 0.7094211123723049 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.56497037551161870000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1872657663724657 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1872657663724357 " " Order of pole (six term test) = 0.9999999999993658 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6299999999999988 " " y[1] (analytic) = 0.7158708568974165 " " y[1] (numeric) = 0.7158708568974164 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.550870543098879500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1819052415485762 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1819052415486058 " " Order of pole (six term test) = 1.00000000000062 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6199999999999988 " " y[1] (analytic) = 0.7223345853799488 " " y[1] (numeric) = 0.7223345853799487 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.53699275529106500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1766052864066177 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1766052864066192 " " Order of pole (six term test) = 1.0000000000000338 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.6099999999999988 " " y[1] (analytic) = 0.7288098535092202 " " y[1] (numeric) = 0.7288098535092201 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.523337012088176000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1713667231059617 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1713667231059621 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5999999999999988 " " y[1] (analytic) = 0.7352941176470597 " " y[1] (numeric) = 0.7352941176470595 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.509903313490211200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1661903789690595 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1661903789690604 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5899999999999987 " " y[1] (analytic) = 0.7417847340701736 " " y[1] (numeric) = 0.7417847340701735 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.49669165949717200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1610770861575033 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1610770861575006 " " Order of pole (six term test) = 0.9999999999999378 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5799999999999987 " " y[1] (analytic) = 0.7482789583956908 " " y[1] (numeric) = 0.7482789583956906 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.96740410021811500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1560276813294734 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.156027681329473 " " Order of pole (six term test) = 0.9999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5699999999999987 " " y[1] (analytic) = 0.7547739452034123 " " y[1] (numeric) = 0.7547739452034122 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.470934485325868500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1510430052782556 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.370587179312271000E-3 " " Order of pole (three term test) = -1.5762066889824748 " " Radius of convergence (six term test) for eq 1 = 1.151043005278253 " " Order of pole (six term test) = 0.9999999999999396 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5599999999999987 " " y[1] (analytic) = 0.7612667478684539 " " y[1] (numeric) = 0.7612667478684537 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.91677793029520800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1461239025515515 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.216574556937487800E-2 " " Order of pole (three term test) = -4.588444431302333 " " Radius of convergence (six term test) for eq 1 = 1.1461239025515524 " " Order of pole (six term test) = 1.0000000000000195 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5499999999999987 " " y[1] (analytic) = 0.767754318618043 " " y[1] (numeric) = 0.7677543186180429 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.446065489574264700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.141271221051332 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.389792512274259400E-2 " " Order of pole (three term test) = -9.574245100927554 " " Radius of convergence (six term test) for eq 1 = 1.1412712210513327 " " Order of pole (six term test) = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5399999999999987 " " y[1] (analytic) = 0.7742335088262629 " " y[1] (numeric) = 0.7742335088262626 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.86792811721170100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.136485811614029 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.126675253867933500E-2 " " Order of pole (three term test) = -15.753539416344596 " " Radius of convergence (six term test) for eq 1 = 1.1364858116140215 " " Order of pole (six term test) = 0.9999999999998277 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5299999999999987 " " y[1] (analytic) = 0.7807010695604661 " " y[1] (numeric) = 0.7807010695604659 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.84416934448472270000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.131768527570898 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.646236257922644000E-3 " " Order of pole (three term test) = -22.08726172067399 " " Radius of convergence (six term test) for eq 1 = 1.131768527570887 " " Order of pole (six term test) = 0.9999999999997531 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5199999999999987 " " y[1] (analytic) = 0.787153652392948 " " y[1] (numeric) = 0.7871536523929478 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.820854660967595000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.127120224288429 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1271202242884142 " " Order of pole (six term test) = 0.9999999999996572 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.5099999999999987 " " y[1] (analytic) = 0.7935878104912317 " " y[1] (numeric) = 0.7935878104912315 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.797984066660317000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1225417586887352 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.122541758688728 " " Order of pole (six term test) = 0.999999999999833 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.49999999999999867 " " y[1] (analytic) = 0.8000000000000008 " " y[1] (numeric) = 0.8000000000000006 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.775557561562888600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1180339887498942 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1180339887498911 " " Order of pole (six term test) = 0.9999999999999272 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.48999999999999866 " " y[1] (analytic) = 0.806386581727281 " " y[1] (numeric) = 0.8063865817272806 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.13036271851296500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1135977729862783 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1135977729862812 " " Order of pole (six term test) = 1.0000000000000657 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.47999999999999865 " " y[1] (analytic) = 0.812743823146945 " " y[1] (numeric) = 0.8127438231469446 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.46407363799516400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.109233969908963 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1092339699089504 " " Order of pole (six term test) = 0.999999999999714 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.46999999999999864 " " y[1] (analytic) = 0.8190679007289713 " " y[1] (numeric) = 0.819067900728971 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.06641387229455700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1049434374663705 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.104943437466346 " " Order of pole (six term test) = 0.9999999999994476 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.45999999999999863 " " y[1] (analytic) = 0.8253549026081224 " " y[1] (numeric) = 0.825354902608122 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.03543864990751460000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1007270324653604 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1007270324653595 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4499999999999986 " " y[1] (analytic) = 0.8316008316008324 " " y[1] (numeric) = 0.8316008316008322 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.67008637422349870000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0965856099730649 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0965856099730646 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4399999999999986 " " y[1] (analytic) = 0.8378016085790894 " " y[1] (numeric) = 0.837801608579089 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.975486606577756700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0925200226998124 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0925200226998117 " " Order of pole (six term test) = 0.9999999999999805 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4299999999999986 " " y[1] (analytic) = 0.8439530762089636 " " y[1] (numeric) = 0.8439530762089633 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.9465097856350400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0885311203635837 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.2905712116828016000E-3 " " Order of pole (three term test) = -0.9192354259660619 " " Radius of convergence (six term test) for eq 1 = 1.0885311203635841 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4199999999999986 " " y[1] (analytic) = 0.8500510030601844 " " y[1] (numeric) = 0.8500510030601841 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.91819909850709860000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0846197490364993 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.286944559081065000E-3 " " Order of pole (three term test) = -2.702818267423937 " " Radius of convergence (six term test) for eq 1 = 1.0846197490364986 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.4099999999999986 " " y[1] (analytic) = 0.8560910880917738 " " y[1] (numeric) = 0.8560910880917735 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.890554545193932000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0807867504739308 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.366061102910220700E-2 " " Order of pole (three term test) = -6.971374245893505 " " Radius of convergence (six term test) for eq 1 = 1.080786750473932 " " Order of pole (six term test) = 1.0000000000000249 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3999999999999986 " " y[1] (analytic) = 0.8620689655172422 " " y[1] (numeric) = 0.8620689655172419 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.86357612569554100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0770329614269003 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.355640687897877200E-2 " " Order of pole (three term test) = -12.903400466577047 " " Radius of convergence (six term test) for eq 1 = 1.0770329614268999 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.38999999999999857 " " y[1] (analytic) = 0.8679802100512117 " " y[1] (numeric) = 0.8679802100512113 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.11635178668256600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0733592129385199 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.93966949962968000E-3 " " Order of pole (three term test) = -19.283096571560414 " " Radius of convergence (six term test) for eq 1 = 1.0733592129385219 " " Order of pole (six term test) = 1.0000000000000533 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.37999999999999856 " " y[1] (analytic) = 0.873820342537575 " " y[1] (numeric) = 0.8738203425375747 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.81161768814308400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0697663296253062 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.1725658598566330000E-4 " " Order of pole (three term test) = -24.706699238026346 " " Radius of convergence (six term test) for eq 1 = 1.0697663296252864 " " Order of pole (six term test) = 0.9999999999995186 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.36999999999999855 " " y[1] (analytic) = 0.879584835957429 " " y[1] (numeric) = 0.8795848359574285 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.04885022678535600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0662551289442874 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.066255128944282 " " Order of pole (six term test) = 0.9999999999998774 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.35999999999999854 " " y[1] (analytic) = 0.8852691218130319 " " y[1] (numeric) = 0.8852691218130316 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.508215857233151400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0628264204469133 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0628264204469147 " " Order of pole (six term test) = 1.0000000000000355 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.34999999999999853 " " y[1] (analytic) = 0.8908685968819607 " " y[1] (numeric) = 0.8908685968819604 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.73867603542521100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.059481005020854 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.059481005020853 " " Order of pole (six term test) = 0.9999999999999769 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3399999999999985 " " y[1] (analytic) = 0.8963786303334537 " " y[1] (numeric) = 0.8963786303334533 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.71569441881547060000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0562196741208711 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0562196741208676 " " Order of pole (six term test) = 0.9999999999999165 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3299999999999985 " " y[1] (analytic) = 0.9017945711966822 " " y[1] (numeric) = 0.9017945711966818 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.69337893602050550000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0530432089900201 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.05304320899002 " " Order of pole (six term test) = 1.0000000000000018 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3199999999999985 " " y[1] (analytic) = 0.9071117561683608 " " y[1] (numeric) = 0.9071117561683604 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.895639449387086000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0499523798725345 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.049952379872531 " " Order of pole (six term test) = 0.9999999999999201 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.3099999999999985 " " y[1] (analytic) = 0.9123255177447321 " " y[1] (numeric) = 0.9123255177447317 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.86766182916653200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.046947945219818 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0469479452198196 " " Order of pole (six term test) = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2999999999999985 " " y[1] (analytic) = 0.9174311926605512 " " y[1] (numeric) = 0.9174311926605508 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.630429290524259000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0440306508910546 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.044030650891056 " " Order of pole (six term test) = 1.0000000000000355 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2899999999999985 " " y[1] (analytic) = 0.9224241306152576 " " y[1] (numeric) = 0.9224241306152573 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.610778342988394000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.041201229350023 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.117351990484153000E-3 " " Order of pole (three term test) = -2.2416272581012273 " " Radius of convergence (six term test) for eq 1 = 1.0412012293500248 " " Order of pole (six term test) = 1.0000000000000444 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2799999999999985 " " y[1] (analytic) = 0.9272997032640957 " " y[1] (numeric) = 0.9272997032640954 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.59179352926730370000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0384603988597731 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.362491104538532700E-2 " " Order of pole (three term test) = -6.348594885031604 " " Radius of convergence (six term test) for eq 1 = 1.0384603988597743 " " Order of pole (six term test) = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.26999999999999846 " " y[1] (analytic) = 0.9320533134495301 " " y[1] (numeric) = 0.9320533134495297 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.764633132481318000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0358088626768933 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.466928572501557400E-2 " " Order of pole (three term test) = -12.290752914748355 " " Radius of convergence (six term test) for eq 1 = 1.0358088626768933 " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = -0.25999999999999845 " " y[1] (analytic) = 0.9366804046459355 " " y[1] (numeric) = 0.9366804046459352 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.555822303269448600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0332473082471587 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.094713846994210700E-2 " " Order of pole (three term test) = -18.64580003963703 " " Radius of convergence (six term test) for eq 1 = 1.033247308247158 " " Order of pole (six term test) = 0.9999999999999822 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.24999999999999845 " " y[1] (analytic) = 0.9411764705882361 " " y[1] (numeric) = 0.9411764705882356 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.718447854656911400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0307764064044147 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.2985609215160516000E-3 " " Order of pole (three term test) = -23.79055438967805 " " Radius of convergence (six term test) for eq 1 = 1.0307764064044123 " " Order of pole (six term test) = 0.9999999999999396 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.23999999999999844 " " y[1] (analytic) = 0.9455370650529508 " " y[1] (numeric) = 0.9455370650529503 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.696687483374259000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0283968105745949 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0283968105745982 " " Order of pole (six term test) = 1.0000000000000853 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.22999999999999843 " " y[1] (analytic) = 0.9497578117580023 " " y[1] (numeric) = 0.9497578117580019 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.675815290511306500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0261091559868274 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.026109155986823 " " Order of pole (six term test) = 0.9999999999998916 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.21999999999999842 " " y[1] (analytic) = 0.9538344143456702 " " y[1] (numeric) = 0.9538344143456697 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.655831276068053700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.023914058893616 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.023914058893613 " " Order of pole (six term test) = 0.9999999999999307 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.2099999999999984 " " y[1] (analytic) = 0.9577626664112638 " " y[1] (numeric) = 0.9577626664112634 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.63673544004450100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0218121158021172 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.021812115802114 " " Order of pole (six term test) = 0.9999999999999201 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.1999999999999984 " " y[1] (analytic) = 0.9615384615384621 " " y[1] (numeric) = 0.9615384615384617 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.618527782440648400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0198039027185566 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.019803902718561 " " Order of pole (six term test) = 1.0000000000001084 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.1899999999999984 " " y[1] (analytic) = 0.9651578033008403 " " y[1] (numeric) = 0.9651578033008398 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 5.75151037907061900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0178899744078431 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.017889974407858 " " Order of pole (six term test) = 1.0000000000003677 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.17999999999999838 " " y[1] (analytic) = 0.9686168151879123 " " y[1] (numeric) = 0.9686168151879118 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 5.73097125311505500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0160708636704427 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.016070863670441 " " Order of pole (six term test) = 0.9999999999999574 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.16999999999999837 " " y[1] (analytic) = 0.971911750413063 " " y[1] (numeric) = 0.9719117504130625 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.56923388014729150000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0143470806385748 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.818976884677249000E-3 " " Order of pole (three term test) = -1.5464337502912424 " " Radius of convergence (six term test) for eq 1 = 1.014347080638574 " " Order of pole (six term test) = 0.9999999999999805 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.15999999999999837 " " y[1] (analytic) = 0.975039001560063 " " y[1] (numeric) = 0.9750390015600624 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 5.693223670277799000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0127191120937726 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.291723654493422700E-2 " " Order of pole (three term test) = -5.045116143579775 " " Radius of convergence (six term test) for eq 1 = 1.0127191120937753 " " Order of pole (six term test) = 1.000000000000064 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.14999999999999836 " " y[1] (analytic) = 0.9779951100244504 " " y[1] (numeric) = 0.9779951100244498 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 5.676015213396110000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.011187420807834 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.594893133601927300E-2 " " Order of pole (three term test) = -10.740186957507522 " " Radius of convergence (six term test) for eq 1 = 1.0111874208078335 " " Order of pole (six term test) = 0.9999999999999893 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.13999999999999835 " " y[1] (analytic) = 0.9807767752059635 " " y[1] (numeric) = 0.9807767752059631 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.52793358363123700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0097524449091468 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.40846475928658300E-2 " " Order of pole (three term test) = -17.146894279601156 " " Radius of convergence (six term test) for eq 1 = 1.0097524449091453 " " Order of pole (six term test) = 0.9999999999999627 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.12999999999999834 " " y[1] (analytic) = 0.9833808634083986 " " y[1] (numeric) = 0.983380863408398 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 5.64492896870660600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0084145972763383 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.744504245742164000E-3 " " Order of pole (three term test) = -22.495161861287812 " " Radius of convergence (six term test) for eq 1 = 1.008414597276339 " " Order of pole (six term test) = 1.0000000000000195 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.11999999999999834 " " y[1] (analytic) = 0.9858044164037859 " " y[1] (numeric) = 0.9858044164037855 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.50484094471903300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0071742649611335 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.007174264961135 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = -0.10999999999999835 " " y[1] (analytic) = 0.9880446596186152 " " y[1] (numeric) = 0.9880446596186148 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.494626892892481500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0060318086422515 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.006031808642248 " " Order of pole (six term test) = 0.9999999999999147 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999983600E-2 " " y[1] (analytic) = 0.9900990099009905 " " y[1] (numeric) = 0.9900990099009901 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.485301019485631000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0049875621120887 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0049875621120885 " " Order of pole (six term test) = 0.9999999999999911 " " " " "TOP MAIN SOLVE Loop" x[1] = -8.99999999999983600E-2 " " y[1] (analytic) = 0.9919650828290847 " " y[1] (numeric) = 0.9919650828290844 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.3576474933738600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0040418317978588 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0040418317978546 " " Order of pole (six term test) = 0.999999999999897 " " " " "TOP MAIN SOLVE Loop" x[1] = -7.99999999999983600E-2 " " y[1] (analytic) = 0.9936406995230527 " " y[1] (numeric) = 0.9936406995230523 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.35198535594827200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.003194896318756 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0031948963187554 " " Order of pole (six term test) = 0.999999999999984 " " " " "TOP MAIN SOLVE Loop" x[1] = -6.99999999999983700E-2 " " y[1] (analytic) = 0.9951238929246694 " " y[1] (numeric) = 0.995123892924669 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.46265246978327760000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0024470060806205 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0024470060806225 " " Order of pole (six term test) = 1.0000000000000462 " " " " "TOP MAIN SOLVE Loop" x[1] = -5.99999999999983700E-2 " " y[1] (analytic) = 0.9964129135113593 " " y[1] (numeric) = 0.996412913511359 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.342659482541421000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0017983829094554 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0017983829094592 " " Order of pole (six term test) = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = -4.999999999999837000E-2 " " y[1] (analytic) = 0.9975062344139651 " " y[1] (numeric) = 0.9975062344139649 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.22599716437343900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0012492197250393 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 7.613684843917159000E-3 " " Order of pole (three term test) = -2.025536108804526 " " Radius of convergence (six term test) for eq 1 = 1.0012492197250398 " " Order of pole (six term test) = 1.000000000000016 " " " " "TOP MAIN SOLVE Loop" x[1] = -3.99999999999983650E-2 " " y[1] (analytic) = 0.9984025559105433 " " y[1] (numeric) = 0.9984025559105429 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.3359981443936700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0007996802557442 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.7408673418305789 " " "Order of pole (ratio test) Not computed" Radius of convergence (three term test) for eq 1 = 1.467967104512271400E-2 " " Order of pole (three term test) = -6.126050238383560 " " Radius of convergence (six term test) for eq 1 = 1.000799680255746 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = -2.99999999999983600E-2 " " y[1] (analytic) = 0.9991008092716556 " " y[1] (numeric) = 0.9991008092716553 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.22244445069463800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0004498987955368 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.76418852961089920E-2 " " Order of pole (three term test) = -12.168588365110512 " " Radius of convergence (six term test) for eq 1 = 1.000449898795536 " " Order of pole (six term test) = 0.9999999999999787 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.99999999999983580E-2 " " y[1] (analytic) = 0.9996001599360256 " " y[1] (numeric) = 0.9996001599360254 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.221334227670013500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000199980003999 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.563971734246556400E-2 " " Order of pole (three term test) = -18.491442915441464 " " Radius of convergence (six term test) for eq 1 = 1.000199980003996 " " Order of pole (six term test) = 0.9999999999999272 " " " " "TOP MAIN SOLVE Loop" x[1] = -9.99999999999835900E-3 " " y[1] (analytic) = 0.9999000099990001 " " y[1] (numeric) = 0.9999000099989999 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.220668093855238000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0000499987500624 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.153560032903266000E-3 " " Order of pole (three term test) = -23.262773321170386 " " Radius of convergence (six term test) for eq 1 = 1.0000499987500648 " " Order of pole (six term test) = 1.0000000000000604 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.6410484082740595000000000000000E-15 " " y[1] (analytic) = 1. " " y[1] (numeric) = 0.9999999999999998 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.22044604925031300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1. " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1. " " Order of pole (six term test) = 1. " " " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000164100E-2 " " y[1] (analytic) = 0.9999000099990001 " " y[1] (numeric) = 0.9999000099989999 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.220668093855238000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0000499987500624 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0000499987500642 " " Order of pole (six term test) = 1.0000000000000426 " " " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000016410E-2 " " y[1] (analytic) = 0.9996001599360256 " " y[1] (numeric) = 0.9996001599360254 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.221334227670013500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000199980003999 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0001999800039976 " " Order of pole (six term test) = 0.9999999999999662 " " " " "TOP MAIN SOLVE Loop" x[1] = 3.000000000000164000E-2 " " y[1] (analytic) = 0.9991008092716553 " " y[1] (numeric) = 0.9991008092716552 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.111222225347319300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.000449898795537 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.000449898795535 " " Order of pole (six term test) = 0.9999999999999538 " " " " "TOP MAIN SOLVE Loop" x[1] = 4.000000000000164500E-2 " " y[1] (analytic) = 0.998402555910543 " " y[1] (numeric) = 0.9984025559105428 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.223998762929113900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0007996802557444 " " Order of pole (given) = 1. " " Radius of convergence (ratio test) for eq 1 = 0.7408673418304643 " " "Order of pole (ratio test) Not computed" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0007996802557442 " " Order of pole (six term test) = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000016400E-2 " " y[1] (analytic) = 0.9975062344139649 " " y[1] (numeric) = 0.9975062344139648 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.112998582186719600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0012492197250393 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0012492197250382 " " Order of pole (six term test) = 0.9999999999999751 " " " " "TOP MAIN SOLVE Loop" x[1] = 6.00000000000016500E-2 " " y[1] (analytic) = 0.9964129135113589 " " y[1] (numeric) = 0.9964129135113587 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.114219827513807400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0017983829094557 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.6964863283173426000E-3 " " Order of pole (three term test) = -0.9450184641384318 " " Radius of convergence (six term test) for eq 1 = 1.0017983829094594 " " Order of pole (six term test) = 1.0000000000000995 " " " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000016400E-2 " " y[1] (analytic) = 0.995123892924669 " " y[1] (numeric) = 0.9951238929246687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.231326234891640000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0024470060806208 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.088517849216482600E-2 " " Order of pole (three term test) = -3.1619596443579168 " " Radius of convergence (six term test) for eq 1 = 1.002447006080625 " " Order of pole (six term test) = 1.000000000000112 " " " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000016400E-2 " " y[1] (analytic) = 0.9936406995230522 " " y[1] (numeric) = 0.993640699523052 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.234656903965515600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0031948963187562 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.761032073083715600E-2 " " Order of pole (three term test) = -8.108146663534857 " " Radius of convergence (six term test) for eq 1 = 1.0031948963187582 " " Order of pole (six term test) = 1.0000000000000497 " " " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000016300E-2 " " y[1] (analytic) = 0.9919650828290842 " " y[1] (numeric) = 0.9919650828290839 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.357647493373861500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.004041831797859 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.008667918831997800E-2 " " Order of pole (three term test) = -14.479735691358822 " " Radius of convergence (six term test) for eq 1 = 1.0040418317978577 " " Order of pole (six term test) = 0.9999999999999716 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000163 " " y[1] (analytic) = 0.9900990099009899 " " y[1] (numeric) = 0.9900990099009895 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.36397576461422500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0049875621120892 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.757690635052084300E-2 " " Order of pole (three term test) = -20.52257450616638 " " Radius of convergence (six term test) for eq 1 = 1.0049875621120885 " " Order of pole (six term test) = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000162 " " y[1] (analytic) = 0.9880446596186143 " " y[1] (numeric) = 0.9880446596186142 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.123656723223121500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.006031808642252 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.070218879635811300E-2 " " Order of pole (three term test) = -24.49679987846839 " " Radius of convergence (six term test) for eq 1 = 1.0060318086422528 " " Order of pole (six term test) = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000162 " " y[1] (analytic) = 0.9858044164037851 " " y[1] (numeric) = 0.9858044164037849 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.252420472359518400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.007174264961134 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.374236623018739200E-3 " " Order of pole (three term test) = -25.223118203902654 " " Radius of convergence (six term test) for eq 1 = 1.0071742649611324 " " Order of pole (six term test) = 0.9999999999999609 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000161 " " y[1] (analytic) = 0.9833808634083977 " " y[1] (numeric) = 0.9833808634083975 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.257971587482644200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0084145972763388 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0084145972763383 " " Order of pole (six term test) = 0.9999999999999876 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000162 " " y[1] (analytic) = 0.9807767752059626 " " y[1] (numeric) = 0.9807767752059625 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.131983395907810200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0097524449091473 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.009752444909146 " " Order of pole (six term test) = 0.9999999999999645 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000163 " " y[1] (analytic) = 0.9779951100244495 " " y[1] (numeric) = 0.9779951100244493 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.27040608535844600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0111874208078344 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0111874208078324 " " Order of pole (six term test) = 0.9999999999999485 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000164 " " y[1] (analytic) = 0.975039001560062 " " y[1] (numeric) = 0.9750390015600617 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.27728946811112220000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0127191120937733 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0127191120937702 " " Order of pole (six term test) = 0.9999999999999218 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000165 " " y[1] (analytic) = 0.9719117504130619 " " y[1] (numeric) = 0.9719117504130618 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.142308470036824400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0143470806385755 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0143470806385768 " " Order of pole (six term test) = 1.000000000000032 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000166 " " y[1] (analytic) = 0.9686168151879111 " " y[1] (numeric) = 0.9686168151879109 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.292388501246024600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0160708636704434 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.584652952820916000E-3 " " Order of pole (three term test) = -1.1143228540228196 " " Radius of convergence (six term test) for eq 1 = 1.0160708636704454 " " Order of pole (six term test) = 1.0000000000000515 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000167 " " y[1] (analytic) = 0.965157803300839 " " y[1] (numeric) = 0.9651578033008389 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 1.150302075814125500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0178899744078438 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.303970722541048500E-2 " " Order of pole (three term test) = -3.855119587486674 " " Radius of convergence (six term test) for eq 1 = 1.0178899744078174 " " Order of pole (six term test) = 0.9999999999993587 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000168 " " y[1] (analytic) = 0.9615384615384609 " " y[1] (numeric) = 0.9615384615384607 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.309263891220327300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0198039027185573 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.027279158155997600E-2 " " Order of pole (three term test) = -9.10751664230588 " " Radius of convergence (six term test) for eq 1 = 1.019803902718563 " " Order of pole (six term test) = 1.0000000000001439 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000169 " " y[1] (analytic) = 0.9577626664112626 " " y[1] (numeric) = 0.9577626664112624 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.318367720022253300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0218121158021178 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.3477713263094402E-2 " " Order of pole (three term test) = -15.570296783041954 " " Radius of convergence (six term test) for eq 1 = 1.0218121158021212 " " Order of pole (six term test) = 1.0000000000000835 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000017 " " y[1] (analytic) = 0.953834414345669 " " y[1] (numeric) = 0.9538344143456686 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.491873457051044600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0239140588936166 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.1777297325513900E-2 " " Order of pole (three term test) = -21.578327238711932 " " Radius of convergence (six term test) for eq 1 = 1.0239140588936164 " " Order of pole (six term test) = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2300000000000017 " " y[1] (analytic) = 0.949757811758001 " " y[1] (numeric) = 0.9497578117580007 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.506861467883485000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.026109155986828 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.55394809793820700E-2 " " Order of pole (three term test) = -25.52307340672742 " " Radius of convergence (six term test) for eq 1 = 1.0261091559868287 " " Order of pole (six term test) = 1.000000000000016 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2400000000000017 " " y[1] (analytic) = 0.9455370650529494 " " y[1] (numeric) = 0.945537065052949 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.696687483374265600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0283968105745958 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.372087421885679000E-3 " " Order of pole (three term test) = -26.326918901678965 " " Radius of convergence (six term test) for eq 1 = 1.028396810574601 " " Order of pole (six term test) = 1.000000000000135 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000017 " " y[1] (analytic) = 0.9411764705882345 " " y[1] (numeric) = 0.9411764705882342 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.538835890992690000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0307764064044156 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.030776406404422 " " Order of pole (six term test) = 1.0000000000001599 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.26000000000000173 " " y[1] (analytic) = 0.9366804046459339 " " y[1] (numeric) = 0.9366804046459336 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.55582230326945470000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0332473082471596 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0332473082471587 " " Order of pole (six term test) = 0.9999999999999769 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000174 " " y[1] (analytic) = 0.9320533134495286 " " y[1] (numeric) = 0.9320533134495281 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.76463313248132570000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0358088626768942 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0358088626768924 " " Order of pole (six term test) = 0.9999999999999627 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000175 " " y[1] (analytic) = 0.9272997032640942 " " y[1] (numeric) = 0.9272997032640937 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.78905803902307900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.038460398859774 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0384603988597756 " " Order of pole (six term test) = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000176 " " y[1] (analytic) = 0.9224241306152561 " " y[1] (numeric) = 0.9224241306152556 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.81437112398453300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.041201229350024 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.041201229350021 " " Order of pole (six term test) = 0.9999999999999307 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000177 " " y[1] (analytic) = 0.9174311926605496 " " y[1] (numeric) = 0.9174311926605492 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.84057238736568700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0440306508910555 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.0028808464333550000E-4 " " Order of pole (three term test) = -0.8988375963930398 " " Radius of convergence (six term test) for eq 1 = 1.0440306508910542 " " Order of pole (six term test) = 0.9999999999999734 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3100000000000018 " " y[1] (analytic) = 0.9123255177447304 " " y[1] (numeric) = 0.91232551774473 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.65074637187490600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.046947945219819 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.065043482864859300E-2 " " Order of pole (three term test) = -2.6141642994262275 " " Radius of convergence (six term test) for eq 1 = 1.046947945219825 " " Order of pole (six term test) = 1.000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000018 " " y[1] (analytic) = 0.907111756168359 " " y[1] (numeric) = 0.9071117561683586 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.89563944938709500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0499523798725354 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.989939875094671200E-2 " " Order of pole (three term test) = -7.022863611942301 " " Radius of convergence (six term test) for eq 1 = 1.0499523798725416 " " Order of pole (six term test) = 1.0000000000001492 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000018 " " y[1] (analytic) = 0.9017945711966805 " " y[1] (numeric) = 0.90179457119668 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.924505248027349300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.053043208990021 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.63463213524044800E-2 " " Order of pole (three term test) = -13.17212747273548 " " Radius of convergence (six term test) for eq 1 = 1.053043208990013 " " Order of pole (six term test) = 0.9999999999998135 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000018 " " y[1] (analytic) = 0.8963786303334519 " " y[1] (numeric) = 0.8963786303334514 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.95425922508730350000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.056219674120872 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.852645426906781400E-2 " " Order of pole (three term test) = -19.691387557926095 " " Radius of convergence (six term test) for eq 1 = 1.0562196741208674 " " Order of pole (six term test) = 0.9999999999998863 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000018 " " y[1] (analytic) = 0.890868596881959 " " y[1] (numeric) = 0.8908685968819585 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.98490138056695800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0594810050208552 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.587758315166359700E-2 " " Order of pole (three term test) = -25.074044589167034 " " Radius of convergence (six term test) for eq 1 = 1.05948100502086 " " Order of pole (six term test) = 1.000000000000119 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000018 " " y[1] (analytic) = 0.8852691218130302 " " y[1] (numeric) = 0.8852691218130297 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.01643171446631300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0628264204469144 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.89518115423789500E-2 " " Order of pole (three term test) = -28.04201044481975 " " Radius of convergence (six term test) for eq 1 = 1.0628264204469198 " " Order of pole (six term test) = 1.0000000000001332 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000018 " " y[1] (analytic) = 0.8795848359574271 " " y[1] (numeric) = 0.8795848359574266 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.048850226785367000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0662551289442885 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 9.341537464348371000E-3 " " Order of pole (three term test) = -27.89481737231003 " " Radius of convergence (six term test) for eq 1 = 1.0662551289442788 " " Order of pole (six term test) = 0.999999999999762 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.38000000000000184 " " y[1] (analytic) = 0.8738203425375732 " " y[1] (numeric) = 0.8738203425375728 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.08215691752412300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0697663296253073 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0697663296253515 " " Order of pole (six term test) = 1.0000000000010818 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000185 " " y[1] (analytic) = 0.8679802100512097 " " y[1] (numeric) = 0.8679802100512093 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.11635178668257800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.073359212938521 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0733592129385205 " " Order of pole (six term test) = 0.9999999999999911 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000185 " " y[1] (analytic) = 0.8620689655172403 " " y[1] (numeric) = 0.8620689655172398 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.43929354282591600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0770329614269014 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0770329614268987 " " Order of pole (six term test) = 0.9999999999999343 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000186 " " y[1] (analytic) = 0.8560910880917719 " " y[1] (numeric) = 0.8560910880917714 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 6.48425757532323600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0807867504739321 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0807867504739306 " " Order of pole (six term test) = 0.9999999999999645 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000187 " " y[1] (analytic) = 0.8500510030601824 " " y[1] (numeric) = 0.850051003060182 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.224265464676143000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0846197490365006 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.084619749036501 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4300000000000019 " " y[1] (analytic) = 0.8439530762089617 " " y[1] (numeric) = 0.8439530762089612 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.26201304751340000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.088531120363585 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.0885311203635872 " " Order of pole (six term test) = 1.0000000000000515 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000019 " " y[1] (analytic) = 0.8378016085790873 " " y[1] (numeric) = 0.8378016085790869 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 3.97548660657776600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0925200226998137 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 8.873774759493951000E-3 " " Order of pole (three term test) = -1.9497016630130386 " " Radius of convergence (six term test) for eq 1 = 1.0925200226998149 " " Order of pole (six term test) = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000019 " " y[1] (analytic) = 0.8316008316008304 " " y[1] (numeric) = 0.8316008316008301 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.00512956133525800000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.0965856099730662 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.940642019597959600E-2 " " Order of pole (three term test) = -5.612647854840901 " " Radius of convergence (six term test) for eq 1 = 1.0965856099730673 " " Order of pole (six term test) = 1.0000000000000213 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000019 " " y[1] (analytic) = 0.8253549026081203 " " y[1] (numeric) = 0.82535490260812 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.03543864990752500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.100727032465362 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.84329930108344800E-2 " " Order of pole (three term test) = -11.255261765009394 " " Radius of convergence (six term test) for eq 1 = 1.1007270324653637 " " Order of pole (six term test) = 1.0000000000000409 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000019 " " y[1] (analytic) = 0.8190679007289692 " " y[1] (numeric) = 0.8190679007289688 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.06641387229456700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1049434374663718 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.42954944866815900E-2 " " Order of pole (three term test) = -17.849147866759253 " " Radius of convergence (six term test) for eq 1 = 1.1049434374665952 " " Order of pole (six term test) = 1.000000000005052 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000019 " " y[1] (analytic) = 0.8127438231469428 " " y[1] (numeric) = 0.8127438231469425 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.09805522849638400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1092339699089646 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.58547387357156500E-2 " " Order of pole (three term test) = -24.153435630958647 " " Radius of convergence (six term test) for eq 1 = 1.1092339699089602 " " Order of pole (six term test) = 0.999999999999897 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.49000000000000193 " " y[1] (analytic) = 0.8063865817272787 " " y[1] (numeric) = 0.8063865817272785 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.753575145675317700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1135977729862798 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.275233133682698400E-2 " " Order of pole (three term test) = -28.945247786104233 " " Radius of convergence (six term test) for eq 1 = 1.1135977729862707 " " Order of pole (six term test) = 0.9999999999997886 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000019 " " y[1] (analytic) = 0.7999999999999988 " " y[1] (numeric) = 0.7999999999999985 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.163336342344343000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1180339887498956 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.554242346823576000E-2 " " Order of pole (three term test) = -31.28209017019486 " " Radius of convergence (six term test) for eq 1 = 1.1180339887498867 " " Order of pole (six term test) = 0.9999999999997993 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000019 " " y[1] (analytic) = 0.7935878104912296 " " y[1] (numeric) = 0.7935878104912293 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.19697609999048600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1225417586887367 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.561161964869037800E-2 " " Order of pole (three term test) = -30.722586450830054 " " Radius of convergence (six term test) for eq 1 = 1.1225417586887338 " " Order of pole (six term test) = 0.9999999999999396 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000019 " " y[1] (analytic) = 0.7871536523929459 " " y[1] (numeric) = 0.7871536523929455 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.23128199145140270000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1271202242884306 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.877271684699916500E-3 " " Order of pole (three term test) = -27.425252860037418 " " Radius of convergence (six term test) for eq 1 = 1.1271202242884262 " " Order of pole (six term test) = 0.999999999999897 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000019 " " y[1] (analytic) = 0.780701069560464 " " y[1] (numeric) = 0.7807010695604637 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.26625401672709570000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1317685275708995 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1317685275708935 " " Order of pole (six term test) = 0.999999999999865 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000019 " " y[1] (analytic) = 0.7742335088262607 " " y[1] (numeric) = 0.7742335088262604 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.30189217581756400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1364858116140306 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.136485811614035 " " Order of pole (six term test) = 1.0000000000000941 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000019 " " y[1] (analytic) = 0.767754318618041 " " y[1] (numeric) = 0.7677543186180407 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.33819646872280640000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1412712210513336 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.141271221051331 " " Order of pole (six term test) = 0.9999999999999396 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000019 " " y[1] (analytic) = 0.7612667478684519 " " y[1] (numeric) = 0.7612667478684515 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 5.83355586059043300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.146123902551553 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.14612390255155 " " Order of pole (six term test) = 0.9999999999999254 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.570000000000002 " " y[1] (analytic) = 0.7547739452034103 " " y[1] (numeric) = 0.75477394520341 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.41280345597761700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1510430052782572 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.1510430052782556 " " Order of pole (six term test) = 0.9999999999999645 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.580000000000002 " " y[1] (analytic) = 0.7482789583956887 " " y[1] (numeric) = 0.7482789583956884 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.45110615032718500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.156027681329475 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.632942179335988600E-3 " " Order of pole (three term test) = -0.9821578051242934 " " Radius of convergence (six term test) for eq 1 = 1.1560276813294765 " " Order of pole (six term test) = 1.000000000000032 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.590000000000002 " " y[1] (analytic) = 0.7417847340701715 " " y[1] (numeric) = 0.7417847340701713 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.99338331899435200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.161077086157505 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.358722927716759800E-2 " " Order of pole (three term test) = -2.8922438976205984 " " Radius of convergence (six term test) for eq 1 = 1.161077086157506 " " Order of pole (six term test) = 1.000000000000023 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.600000000000002 " " y[1] (analytic) = 0.7352941176470575 " " y[1] (numeric) = 0.7352941176470573 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.01980662698043100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.166190378969061 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.49911569053203200E-2 " " Order of pole (three term test) = -7.0444229273503485 " " Radius of convergence (six term test) for eq 1 = 1.1661903789690626 " " Order of pole (six term test) = 1.0000000000000355 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.610000000000002 " " y[1] (analytic) = 0.7288098535092182 " " y[1] (numeric) = 0.7288098535092179 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.570011036264539600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1713667231059632 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.52688094921119200E-2 " " Order of pole (three term test) = -12.86449539036531 " " Radius of convergence (six term test) for eq 1 = 1.1713667231059635 " " Order of pole (six term test) = 1.0000000000000036 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.620000000000002 " " y[1] (analytic) = 0.7223345853799467 " " y[1] (numeric) = 0.7223345853799464 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.07398551058213900000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1766052864066192 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.29563355041835400E-2 " " Order of pole (three term test) = -19.530047181402704 " " Radius of convergence (six term test) for eq 1 = 1.1766052864066234 " " Order of pole (six term test) = 1.0000000000000888 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.630000000000002 " " y[1] (analytic) = 0.7158708568974145 " " y[1] (numeric) = 0.7158708568974141 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 4.652611629296652000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.181905241548578 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.69058615799615300E-2 " " Order of pole (three term test) = -26.070611642049105 " " Radius of convergence (six term test) for eq 1 = 1.1819052415485942 " " Order of pole (six term test) = 1.0000000000003464 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.640000000000002 " " y[1] (analytic) = 0.7094211123723029 " " y[1] (numeric) = 0.7094211123723027 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.12994075102324740000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1872657663724675 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.64820623368000340E-2 " " Order of pole (three term test) = -31.506076536465137 " " Radius of convergence (six term test) for eq 1 = 1.1872657663724675 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.650000000000002 " " y[1] (analytic) = 0.7029876977152887 " " y[1] (numeric) = 0.7029876977152885 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.15858450505857600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1926860441876574 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.1703132663172300E-2 " " Order of pole (three term test) = -35.008589982962846 " " Radius of convergence (six term test) for eq 1 = 1.1926860441876417 " " Order of pole (six term test) = 0.9999999999996643 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.660000000000002 " " y[1] (analytic) = 0.6965728615213138 " " y[1] (numeric) = 0.6965728615213136 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.18767234830375500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.1981652640600138 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.32715426588854300E-2 " " Order of pole (three term test) = -36.053659680805566 " " Radius of convergence (six term test) for eq 1 = 1.1981652640600187 " " Order of pole (six term test) = 1.0000000000001066 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.670000000000002 " " y[1] (analytic) = 0.6901787562978798 " " y[1] (numeric) = 0.6901787562978796 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.217204280758785000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2037026210821353 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.246396053241022700E-2 " " Order of pole (three term test) = -34.51723185644925 " " Radius of convergence (six term test) for eq 1 = 1.2037026210821276 " " Order of pole (six term test) = 0.9999999999998348 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.680000000000002 " " y[1] (analytic) = 0.683807439824944 " " y[1] (numeric) = 0.6838074398249437 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.247180302423664500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.209297316626479 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.089818790245367800E-2 " " Order of pole (three term test) = -30.687422347842528 " " Radius of convergence (six term test) for eq 1 = 1.2092973166264447 " " Order of pole (six term test) = 0.9999999999992752 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.6900000000000021 " " y[1] (analytic) = 0.677460876634373 " " y[1] (numeric) = 0.6774608766343728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.27760041329839400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2149485585818038 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 2.41651991967787400000E-4 " " Order of pole (three term test) = -25.18904938975635 " " Radius of convergence (six term test) for eq 1 = 1.2149485585820974 " " Order of pole (six term test) = 1.000000000006283 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000021 " " y[1] (analytic) = 0.6711409395973141 " " y[1] (numeric) = 0.6711409395973139 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.30846461338297260000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2206555615733714 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.220655561573346 " " Order of pole (six term test) = 0.99999999999946 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000021 " " y[1] (analytic) = 0.6648494116082695 " " y[1] (numeric) = 0.6648494116082692 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.00965935401610300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2264175471673597 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2264175471673506 " " Order of pole (six term test) = 0.9999999999998082 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000021 " " y[1] (analytic) = 0.6585879873551094 " " y[1] (numeric) = 0.658587987355109 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.05728792177252300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2322337440599502 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2322337440599462 " " Order of pole (six term test) = 0.9999999999999147 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000021 " " y[1] (analytic) = 0.6523582751647192 " " y[1] (numeric) = 0.6523582751647189 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.10558262334371700000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.238103388251564 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2381033882515622 " " Order of pole (six term test) = 0.9999999999999645 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000021 " " y[1] (analytic) = 0.6461617989144468 " " y[1] (numeric) = 0.6461617989144466 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.43636230581979200000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2440257232067202 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" "NO REAL POLE (three term test) for Equation 1" Radius of convergence (six term test) for eq 1 = 1.2440257232067178 " " Order of pole (six term test) = 0.9999999999999467 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000021 " " y[1] (analytic) = 0.6399999999999987 " " y[1] (numeric) = 0.6399999999999985 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.46944695195362140000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2500000000000013 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.697314411161098000E-3 " " Order of pole (three term test) = -1.225665159192751 " " Radius of convergence (six term test) for eq 1 = 1.250000000000002 " " Order of pole (six term test) = 1.0000000000000124 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000021 " " y[1] (analytic) = 0.6338742393509115 " " y[1] (numeric) = 0.6338742393509113 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.50297568729730100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2560254774486077 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.74404651683051200E-2 " " Order of pole (three term test) = -3.473710305318223 " " Radius of convergence (six term test) for eq 1 = 1.256025477448608 " " Order of pole (six term test) = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7700000000000021 " " y[1] (analytic) = 0.6277857994852143 " " y[1] (numeric) = 0.6277857994852141 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.53694851185083100000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2621014222319866 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.00427024600149600E-2 " " Order of pole (three term test) = -7.634929528561885 " " Radius of convergence (six term test) for eq 1 = 1.262101422231987 " " Order of pole (six term test) = 1.0000000000000089 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7800000000000021 " " y[1] (analytic) = 0.6217358865953729 " " y[1] (numeric) = 0.6217358865953727 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.57136542561421130000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2682271089990165 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.22644479704747670E-2 " " Order of pole (three term test) = -13.299541232856404 " " Radius of convergence (six term test) for eq 1 = 1.2682271089990174 " " Order of pole (six term test) = 1.000000000000016 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.7900000000000021 " " y[1] (analytic) = 0.6157256326580862 " " y[1] (numeric) = 0.615725632658086 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.606226428587442000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2744018204632335 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.28721405825065400E-2 " " Order of pole (three term test) = -19.899094338876242 " " Radius of convergence (six term test) for eq 1 = 1.2744018204632315 " " Order of pole (six term test) = 0.9999999999999627 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000022 " " y[1] (analytic) = 0.6097560975609744 " " y[1] (numeric) = 0.609756097560974 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.462297281155781000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2806248474865711 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.0752533597185600E-2 " " Order of pole (three term test) = -26.752697644733484 " " Radius of convergence (six term test) for eq 1 = 1.280624847486579 " " Order of pole (six term test) = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8100000000000022 " " y[1] (analytic) = 0.6038282712396582 " " y[1] (numeric) = 0.6038282712396579 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 5.515921053245176000000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2868954891520925 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.50374669697253400E-2 " " Order of pole (three term test) = -33.13187360445268 " " Radius of convergence (six term test) for eq 1 = 1.2868954891520912 " " Order of pole (six term test) = 0.9999999999999769 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000022 " " y[1] (analytic) = 0.5979430758191807 " " y[1] (numeric) = 0.5979430758191805 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.713473972766231400000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2932130528261783 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.52223960022397200E-2 " " Order of pole (three term test) = -38.34210777039979 " " Radius of convergence (six term test) for eq 1 = 1.293213052826168 " " Order of pole (six term test) = 0.9999999999998046 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000022 " " y[1] (analytic) = 0.5921013677541582 " " y[1] (numeric) = 0.592101367754158 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.750111332578861500000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.2995768542106325 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 6.1252635926375600E-2 " " Order of pole (three term test) = -41.811381388237464 " " Radius of convergence (six term test) for eq 1 = 1.2995768542106378 " " Order of pole (six term test) = 1.0000000000001101 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000022 " " y[1] (analytic) = 0.5863039399624753 " " y[1] (numeric) = 0.5863039399624751 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.78719278160134230000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.305986217385162 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 5.355044023818532000E-2 " " Order of pole (three term test) = -43.16907326170791 " " Radius of convergence (six term test) for eq 1 = 1.3059862173851695 " " Order of pole (six term test) = 1.0000000000001492 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8500000000000022 " " y[1] (analytic) = 0.5805515239477491 " " y[1] (numeric) = 0.5805515239477489 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.824718319833672600000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3124404748406702 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 4.29671461274046600E-2 " " Order of pole (three term test) = -42.29672610982208 " " Radius of convergence (six term test) for eq 1 = 1.3124404748406686 " " Order of pole (six term test) = 0.9999999999999716 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8600000000000022 " " y[1] (analytic) = 0.5748447919061841 " " y[1] (numeric) = 0.5748447919061839 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.86268794727585300000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3189389675038052 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 3.066504508895224000E-2 " " Order of pole (three term test) = -39.33766601226025 " " Radius of convergence (six term test) for eq 1 = 1.318938967503797 " " Order of pole (six term test) = 0.9999999999998366 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.8700000000000022 " " y[1] (analytic) = 0.5691843588138186 " " y[1] (numeric) = 0.5691843588138183 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 3.90110166392788340000000000000E-14 "%" Correct digits = 17 h = 1.00E-2 " " Radius of convergence (given) for eq 1 = 1.3254810447531884 " " Order of pole (given) = 1. " " "NO POLE (ratio test) for Equation 1" Radius of convergence (three term test) for eq 1 = 1.79546039240427420E-2 " " Order of pole (three term test) = -34.66379288989032 " " Radius of convergence (six term test) for eq 1 = 1.325481044753185 " " Order of pole (six term test) = 0.9999999999999343 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" Iterations = 288 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 54 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 6 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 6 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 3 Minutes 7 Seconds "Time to Timeout " Unknown Percent Done = 96.33333333333341 "%" (%o58) true (%o58) diffeq.max