I have to compute the two dimensional fourier transform of the following function: $f(x,y,z) = \frac{x}{(x^{2}+y^{2}+z^{2})^{5/2}}$
the paper that i'm following defined the two dimensional fourier transform of a function $g(x,y,z)$ as:
$\hat{g}(k_{1},k_{2},z)=\frac{1}{2\pi}\int \int g(x,y,z) e^{ik_{1}x+ik_{2}y}dxdy$
any idea on how to proceed? I'm also interested in the procedure that it is required to obtain the fourier transform, as I have to apply it to other functions.
It might be useful to say that the the authors also give an example, in particular given: $g(x,y,z) = \frac{1}{(x^{2}+y^{2}+z^{2})^{1/2}}$
the fourier transform according to the definition they gave is: $\hat{g}(k_{1},k_{2},z)= \frac{1}{k_{1}^{2}+k_{2}^{2}}e^{-kz}$
i'm quite clueless to be honest...