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Help with Integrals with four Hankel functions

  1. Aug 27, 2010 #1
    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

    [tex]\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)[/tex]

    where [tex]n\in i \mathbb{R}, p_i\in \mathbb{R}[/tex].

    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

    [tex]\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)[/tex]

    i.e. x and y reversed for [tex]p_0[/tex]

    Any help would be welcome.
  2. jcsd
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