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Fourier transform of Bessel functions

  1. Aug 14, 2009 #1
    Hi there,

    I am calculating the Fourier transform of the bessel function [tex]J_0^2(bx)[/tex] by using Maple. I tried two equations and get two results.

    [tex]\int J_0^2(bx)e^{-j2\pi fx}dx=G^{2, 1}_{2, 2}\left(-1/4\,{\frac {{w}^{2}}{{b}^{2}}}\, \Big\vert\,^{1/2, 1/2}_{0, 0}\right)
    {\pi }^{-1}{b}^{-1}[/tex]

    and

    [tex]\int J_0^2(bx)[cos(2\pi fx)-jsin(2\pi fx)]dx=G^{2, 0}_{2, 2}\left(1/4\,{\frac {{w}^{2}}{{b}^{2}}}\, \Big\vert\,^{1/2, 1/2}_{0, 0}\right)
    {b}^{-1}[/tex]

    I tried to plot these two functions but only the second one shows a plot. The first one does not show anything and it tells that could not evaluate the function in the variable range (e.g. 0..4).

    Could anyone help me to verify this? I want to make sure that the two results are identical. If it is not, which one is correct so I may continue with other calculations of FFT on the bessel functions and on the Generalized geometric functions.


    Thanks so much in advance.

    VietHa
     
  2. jcsd
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