%-----------------------------------------------------------------------
% 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 definition gives:        ',  num2str(besintj0(x))])
      disp(['Compare to Matlab''s bessel(0,x) = ', num2str(bessel(0,x))])