A problem about integral of modified bessel function

[jianingli]

To calculate a p.d.f. of a r.v., I need to integral a product of two bessel function as

$$\mathcal{L}^{-1} \left( abs^2 K_n( \sqrt{as}) K_n( \sqrt{bs} ) \right)$$

where $$\mathcal{L}^{-1}$$ is the inverse Laplace transform.

I think some properties about the bessel function can solve this integral, but I cannot find it. So, please help me.

Thank you very much.

 

[birisi11]

I am looking for the inverse laplace transform of modified Bessel functions, could you please help me?.