Fourier transform in arbitrary dimension?

*To*: mathgroup at smc.vnet.net*Subject*: [mg88066] Fourier transform in arbitrary dimension?*From*: Barrow <GRseminar at gmail.com>*Date*: Wed, 23 Apr 2008 04:09:50 -0400 (EDT)

Dear all, I would like to calculate a Fourier transform in arbitrary dimension , say D, of the function 1/q^2, where q denotes the absolute value of a D dimensional spatial vector. The integral I have to perform is \int \frac{d^Dq}{(2\pi)^D}\exp(-iQ\cdot x)\frac{1}{q^2} where |Q| = q. But I can't find a way to tell Mathematica to calculate this integral "of dimension D." PS. The answer is proportional to \Gamma(D/2 - 1)(x^2/4)^{1-D/2} Any ideas would be appreciated. Sincerely Barrow