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I found in an article "Imperfect Bose Gas with Hard-Sphere Interaction", Phys. Rev. 105, 776–784 (1957) the following integral, but I don't know how to solve it. Any hints?

$$\int_0^\infty {\int_0^\infty {\mathrm dp\mathrm dq\frac{\sinh(upq)}{q^2 - p^2}pq} } e^{-vq^2 - wp^2} = \frac{\pi}{4}\frac{u(w - v)}{\left[(w + v)^2-u^2 \right]\left(4wv-u^2\right)^{1/2}}$$

for $u,v,w > 0$.

  • 1
    Aren't there supposed to be restrictions on $u,v,$ and $w$?2011-09-11
  • 0
    i think the only restrictions are that the quantity in the square root is positive and the denominator don't vanish!2011-09-11
  • 0
    If $v$ or $w$ are negative, for instance...2011-09-11
  • 0
    I think $u$ and $v$ should both be positive, for convergence of the double integral.2011-09-11
  • 2
    u,v and w are defined in the article, they are positive!2011-09-11
  • 0
    i want to tell you that there is a mistake. THe quantity in the square root is $4wv-u^2$2011-09-11
  • 2
    ...and those are the restrictions I was talking about. I've edited in your correction on the rooted portion.2011-09-11

3 Answers 3