Homework Help: Integration of the product of sine and the first Bessel function

1. Oct 12, 2011

Ardat

1. The problem statement, all variables and given/known data

I'm supposed to prove that:

$\int_0^∞[STRIKE][/STRIKE]$sin(ka)J0(kp)dk = (a2 - p2)1/2 if p < a
and = 0 if p > a

J0 being the first Bessel function.

2. Relevant equations

3. The attempt at a solution

I've tried to inverse the order of integration and then make the integral form of the delta Dirac function appear, but I'm not sure how to do it, and so far my attemps have failed.

I also tried to put both sine and the bessel function as their series form, then transfom the infinite series into a limit of a finite series so I can interchange the sum and the integral, but it doesn't really leads me anywhere.

If anyone could give me some advise on how to resolve this, I would be grateful.

2. Oct 13, 2011

Ardat

Nobody can help me?