# Fourier transform of Bessel functions

1. Aug 14, 2009

### vietha

Hi there,

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

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

and

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

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.