How can I evalute this integral?
$\psi(z)=\int\limits_{-\infty}^\infty\int\limits_{-\infty}^\infty [(x-a)^2+(y-b)^2+z^2]^{-3\over 2}f(x,y)\,\,\,dxdy\;.$
I think we can treat $z$ as a constant and take it out of the integral or something. Maybe changing variables like taking $u={1\over z}[(x-a)^2+(y-b)^2]$? But then how do I change $f(x,y)$ which is some arbitrary function, etc?
Thanks.