When calculating the screened Coulomb potential energy between electrons in cylindrical coordinates (need those for my particular geometry) the following triple integral always appears,
$$\int_0^\infty dr r J_m(qr)\int_{-\infty}^\infty dze^{ipz}\int_0^{2\pi}d\phi e^{im\phi}\frac{e^{-\mu\sqrt{r^2+a^2-2ra\cos\phi+z^2}}}{\sqrt{r^2+a^2-2ra\cos\phi+z^2}}$$ where $m$ is a positive integer, $p,q,\mu$ are real numbers $(p,\mu>0)$, and $J_m$ is the first order Bessel function of order $m$. It surprises me to find practically no reference to this kind of integral in the literature. Does anyone have a clue as to how one can solve/estimate it?
Thanks!