- #1

bobred

- 173

- 0

## Homework Statement

Noting that [itex]J_0(k)[/itex] is an even function of [itex]k[/itex], use the result of part (a) to

obtain the Fourier transform of the Bessel function [itex]J_0(x)[/itex].

## Homework Equations

In (a) I am asked to show that the Fourier transform of

[tex]f(x)=\dfrac{1}{\sqrt{1-x^{2}}}[/tex]

is

[tex]\tilde{f}(k)=\sqrt{\pi/2}J_0(-k)[/tex]

where

[tex]J_0(x)=\frac{1}{\pi}\int_{0}^{\pi} e^{i x \cos \theta}d \theta[/tex]

## The Attempt at a Solution

I have found the Fourier transform of [itex]f(x)[/itex] using trig substitution I just cant see how to get the FT of [itex]J_0(x)[/itex].

Any hints as to where I should begin?