       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

```

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