Integral recurrence relation

From: Darragh (darragh.oneill_at_gmail.com)
Date: 10/27/04 

Date: Wed, 27 Oct 2004 13:30:08 +0000 (UTC)

I have encountered the following integral in some research in the
physical sciences

   \int |u-A|^(2a) |u-B|^(2b) Exp[-|u|^2] du

where u, A and B are cartesian vectors in 3 dimensions and the
integral is to performed over all space. This seems like quite a
straightforward integral but the best I can do is to write it as a
triple infinite series in A^2, B^2 and |A-B|^2 (which quickly
truncates, depending on the values of a and b). I was wondering if
anyone has any suggestions as how I might produce a more useful
formulation.

Even more useful would be a suggestion as to how I might derive a
recurrence relation to generate integrals of higher values of a and b
or if it is possible to prove or disprove the existence of such a
relation.

Thanks in advance,

Darragh

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