I'm trying to calculate the 2D fourier transform of this function:
$\frac{1}{(x^2+y^2+z^2)^{3/2}}$
I only want to do the fourier transform for x and y (and leave z as it is).
So far, I've tried using the method of residues (assuming $k_x$ > 0 and closing the contour on the top), but I'm left with $\frac{e^{ik_x x}}{[(x - ic)(x+ic)]^{3/2}}$
(where c depends only on y and z). And because of the fractional power on the bottom I'm not sure how to get the residue. I've also tried using polar coordinates but that didn't get me anywhere. Does anyone know how I should proceed?
Also, I know the answer should look like $e^{- \sqrt{k_x^2 + k_y^2}z}$.