function [ n_data, x, fx ] = bessel_i0_values ( n_data ) %*****************************************************************************80 % %% BESSEL_I0_VALUES returns some values of the I0 Bessel function. % % Discussion: % % The modified Bessel functions In(Z) and Kn(Z) are solutions of % the differential equation % % Z^2 W'' + Z * W' - ( Z^2 + N^2 ) * W = 0. % % The modified Bessel function I0(Z) corresponds to N = 0. % % In Mathematica, the function can be evaluated by: % % BesselI[0,x] % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 15 September 2004 % % Author: % % John Burkardt % % Reference: % % Milton Abramowitz and Irene Stegun, % Handbook of Mathematical Functions, % US Department of Commerce, 1964. % % Stephen Wolfram, % The Mathematica Book, % Fourth Edition, % Wolfram Media / Cambridge University Press, 1999. % % Parameters: % % Input/output, integer N_DATA. The user sets N_DATA to 0 before the % first call. On each call, the routine increments N_DATA by 1, and % returns the corresponding data; when there is no more data, the % output value of N_DATA will be 0 again. % % Output, real X, the argument of the function. % % Output, real FX, the value of the function. % n_max = 20; fx_vec = [ ... 0.1000000000000000E+01, ... 0.1010025027795146E+01, ... 0.1040401782229341E+01, ... 0.1092045364317340E+01, ... 0.1166514922869803E+01, ... 0.1266065877752008E+01, ... 0.1393725584134064E+01, ... 0.1553395099731217E+01, ... 0.1749980639738909E+01, ... 0.1989559356618051E+01, ... 0.2279585302336067E+01, ... 0.3289839144050123E+01, ... 0.4880792585865024E+01, ... 0.7378203432225480E+01, ... 0.1130192195213633E+02, ... 0.1748117185560928E+02, ... 0.2723987182360445E+02, ... 0.6723440697647798E+02, ... 0.4275641157218048E+03, ... 0.2815716628466254E+04 ]; x_vec = [ ... 0.00E+00, ... 0.20E+00, ... 0.40E+00, ... 0.60E+00, ... 0.80E+00, ... 0.10E+01, ... 0.12E+01, ... 0.14E+01, ... 0.16E+01, ... 0.18E+01, ... 0.20E+01, ... 0.25E+01, ... 0.30E+01, ... 0.35E+01, ... 0.40E+01, ... 0.45E+01, ... 0.50E+01, ... 0.60E+01, ... 0.80E+01, ... 0.10E+02 ]; if ( n_data < 0 ) n_data = 0; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; x = 0.0; fx = 0.0; else x = x_vec(n_data); fx = fx_vec(n_data); end return end