Services & ResourcesWolfram ForumsMathGroup Archive

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



• Prev by Date: Re: waveform
• Next by Date: Re: waveform
• Previous by thread: Re: When Find finds something -
• Next by thread: Re: Fourier transform in arbitrary dimension?