bessel functions with octave

[john]

Hi,

here are the other programs .I did little changes alo compare with
16/08/2001)

      function y=besintj0(x)
%-----------------------------------------------------------------------
% Approximate the Bessel's function of the first kind of order zero
% via the following integral definition.
%   J0(x) = (1/pi)*integral (from 0 to pi) of cos(x*sin(q))*dq
% Programming Note:
%   For large values of x, apply the asymptotic approximation formula.
%     J0(x)=sqrt(2/pi/x)*cos(x-pi/4),  for x>25
% Instructor: Nam Sun Wang
%-----------------------------------------------------------------------

      global x
%     pi = 3.141593  already defined in Matlab

% Pass x into the integrand through "common"
      

% Call an integration routine to do the grunt work.
%     y = 1/pi * quad8('bintegra', 0, pi);  ... old
      y = 1/pi * quadl(@bintegra, 0, pi);

------------------------------------------------------------------------------------------------

%-----------------------------------------------------------------------
% Approximate the Bessel function of the first kind of order 0
% via Taylor's series expansion.
% Instructor: Nam Sun Wang
%-----------------------------------------------------------------------

% Start fresh ----------------------------------------------------------
      clear all

% Print out a program header -------------------------------------------
      disp("Approximate the Bessel function via Taylor''s series ")
      disp("expansion, which fails for x far away from the point ")
      disp("of expansion around x=0.  This program is accurate to ")
      disp("about 5 significant figures for 0<x<10.")
      disp(' ')

% Input data -----------------------------------------------------------
      x = input("Enter x: ");

% Print out the results ------------------------------------------------
      disp(' ')
      disp(["Taylor''s series expansion gives:  ", num2str(besj0(x))   ]) 
          disp(["integral def gives:                ", num2str(besintj0(x))])
          disp(["Compare to Matlab''s bessel(0,x) = ", num2str(besselj(0,x))])

---------------------------------------------------------------------------------------

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