- #1
bobred
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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 can't see how to get the FT of [itex]J_0(x)[/itex].
Any hints as to where I should begin?