function [ n_data, nu, x, fx ] = bessel_ix_values ( n_data ) %*****************************************************************************80 % %% BESSEL_IX_VALUES returns some values of the Ix Bessel function. % % Discussion: % % This set of data considers the less common case in which the % index of the Bessel function In is actually not an integer. % We may suggest this case by occasionally replacing the symbol % "In" by "Ix". % % 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. % % In Mathematica, the function can be evaluated by: % % BesselI[n,x] % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 March 2007 % % Author: % % John Burkardt % % Reference: % % Milton Abramowitz, Irene Stegun, % Handbook of Mathematical Functions, % National Bureau of Standards, 1964, % ISBN: 0-486-61272-4, % LC: QA47.A34. % % Stephen Wolfram, % The Mathematica Book, % Fourth Edition, % Cambridge University Press, 1999, % ISBN: 0-521-64314-7, % LC: QA76.95.W65. % % 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 NU, the order of the function. % % Output, real X, the argument of the function. % % Output, real FX, the value of the function. % n_max = 28; fx_vec = [ ... 0.3592084175833614E+00, ... 0.9376748882454876E+00, ... 2.046236863089055E+00, ... 3.053093538196718E+00, ... 4.614822903407601E+00, ... 26.47754749755907E+00, ... 2778.784603874571E+00, ... 4.327974627242893E+07, ... 0.2935253263474798E+00, ... 1.099473188633110E+00, ... 21.18444226479414E+00, ... 2500.906154942118E+00, ... 2.866653715931464E+20, ... 0.05709890920304825E+00, ... 0.3970270801393905E+00, ... 13.76688213868258E+00, ... 2028.512757391936E+00, ... 2.753157630035402E+20, ... 0.4139416015642352E+00, ... 1.340196758982897E+00, ... 22.85715510364670E+00, ... 2593.006763432002E+00, ... 2.886630075077766E+20, ... 0.03590910483251082E+00, ... 0.2931108636266483E+00, ... 11.99397010023068E+00, ... 1894.575731562383E+00, ... 2.716911375760483E+20 ]; nu_vec = [ ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 0.50E+00, ... 1.50E+00, ... 1.50E+00, ... 1.50E+00, ... 1.50E+00, ... 1.50E+00, ... 2.50E+00, ... 2.50E+00, ... 2.50E+00, ... 2.50E+00, ... 2.50E+00, ... 1.25E+00, ... 1.25E+00, ... 1.25E+00, ... 1.25E+00, ... 1.25E+00, ... 2.75E+00, ... 2.75E+00, ... 2.75E+00, ... 2.75E+00, ... 2.75E+00 ]; x_vec = [ ... 0.2E+00, ... 1.0E+00, ... 2.0E+00, ... 2.5E+00, ... 3.0E+00, ... 5.0E+00, ... 10.0E+00, ... 20.0E+00, ... 1.0E+00, ... 2.0E+00, ... 5.0E+00, ... 10.0E+00, ... 50.0E+00, ... 1.0E+00, ... 2.0E+00, ... 5.0E+00, ... 10.0E+00, ... 50.0E+00, ... 1.0E+00, ... 2.0E+00, ... 5.0E+00, ... 10.0E+00, ... 50.0E+00, ... 1.0E+00, ... 2.0E+00, ... 5.0E+00, ... 10.0E+00, ... 50.0E+00 ]; if ( n_data < 0 ) n_data = 0; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; nu = 0.0; x = 0.0; fx = 0.0; else nu = nu_vec(n_data); x = x_vec(n_data); fx = fx_vec(n_data); end return end