# Help with Integrals with four Hankel functions

1. Aug 27, 2010

### betel

I have some nasty Integrals involving a couple of Hankel Functions. I've been trying for some time to do them but I dont't get on.
The (double) integral is

$$\int_0^\infty dx\int_0^\infty dy\ x^2 y^2\ \prod_{j=0}^{3} H_n^{(1)}(p_j x)H_n^{(2)}(p_j y)$$

where $$n\in i \mathbb{R}, p_i\in \mathbb{R}$$.

As the complete solution seem so to be quite complicated, I would be happy if I could do even one of the integrals. Or if I Could compare the above integral to

$$\int_0^\infty dx\int_0^\infty dy\ x^2 y^2 H_n^{(2)}(p_0 x)H_n^{(1)}(p_0 y)\ \prod_{j=1}^{3} H_n^{(1)}(p_j x)H_n^{(2)}(p_j y)$$

i.e. x and y reversed for $$p_0$$

Any help would be welcome.