Re: Help with 3 dimensional Fourier Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg90463] Re: Help with 3 dimensional Fourier Integral
- From: David Wood <dmwood at comcast.net>
- Date: Thu, 10 Jul 2008 06:34:39 -0400 (EDT)
- References: <g51ue7$6uv$1@smc.vnet.net>
bye from <fireyend at yahoo.com> wrote: > int > dk^3 exp[i k.x]/(k^2(k+q)^2) > > Here k=(k1,k2,k3), x=(x1,x2,x3), > q=(q1,q2,q3), k^2=k1^2+k2^2+k3^2, q is arbitrary, with the usual dot product. Customarily, one would first align the kz axis with the `external' vector x, resulting in the argument of the exponential's becoming I |k| |x| cos(ang between k and x). Then integrate over the azimuthal angle (giving a factor of 2 pi), then over the angle between k and x. The resulting function should be more manageable, and I think coughs up a difference betwen two logs. Hope this helps. -- D. M. Wood wood43 at comcast.net