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MathGroup Archive 2008

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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


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