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