Solve Laplace Transform: Find Series Solution

[ber70]

How can I solve this Laplace transform (or how can I find series solution)?
http://www.forkosh.dreamhost.com/mathtex.cgi?M=\int[/URL] _0^{\infty }e^{-\text{kR}}J_1^2(\text{ka})dk[/PLAIN] ;R>2a

 

[ber70]

J(ka) is spherical bessel function (please help).

 

[gabbagabbahey]

Is this part of a larger problem? If you are simply looking to evaluate this integral, I'd recommend you use Rayleigh's formula.

 

[ber70]

This is jackson classicsal electrodynamics problem 5.34b (third edition). I expand J1(ka) and integrate each term of J1(ka)*J1(ka) but I can't find solution. What must I do if R>2a? (please help).

 

[ber70]

Thanks for all. I found the answer :)