Re: Fourier transform in arbitrary dimension?

*To*: mathgroup at smc.vnet.net*Subject*: [mg88079] Re: Fourier transform in arbitrary dimension?*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 23 Apr 2008 06:05:54 -0400 (EDT)*Organization*: Uni Leipzig*References*: <fumr2o$sh2$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, integrateDimD[f_, dim_Integer] := Module[{var}, var = Table[{Unique[x], -Infinity, Infinity}, {dim}]; Integrate @@ {f @@ (First /@ var), Sequence @@ var} ] and integrateDimD[f, 3] gives Integrate[f[x$12006, x$12007, x$12008], {x$12006, -Infinity, Infinity}, {x$12007, -Infinity, Infinity}, {x$12008, -Infinity, Infinity}] Regards Jens Barrow wrote: > 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 >