From: Jean-Philippe Grivet <grivet@cnrs-orleans.fr>
Subject: Re: Integral of THREE Spherical Harmonics/Legendre Functions
Date: Fri, 26 Mar 1999 10:03:05 +0100
Newsgroups: sci.math.num-analysis,sci.math

i-carron@news.tamu.edu wrote:
> 
> Hello,
> 
> I am looking for the integral of three sperical harmonics. Does anybody
> know a reference for this. Hobson gives the integral of a product of
> three legendre polynomials... a comparable result would be of interest
> for an integral of three legendre functions.

Hi,
The integral of a product of three spherical harmonics Y_j_1*Y_j_2*Y_j_3
is given in most quantum mechanics books; the one I have here (BH
Bransden and CJ Joachain, Physics of atoms and molecules, Longman,
Appendix 4) shows that it is proportional to the product of two
Clebsch-Gordan coefficients, <j_1 j_2 0 0/j_3 0>*<j_1 j_2 m_1 m_2/j_3
-m_3>.
HTH,
JP Grivet
-- 
********************************************************
Jean-Philippe GRIVET, Centre de Biophysique Moleculaire
rue Charles-Sadron, 45071 Orleans cedex 02, France
Telephone: 02 38 25 76 32  Telecopie: 02 38 63 15 17   
e-mail: grivet@cnrs-orleans.fr                         
********************************************************