product of Spher.Harmonics

*To*: mathgroup at smc.vnet.net*Subject*: [mg4515] product of Spher.Harmonics*From*: Vandemoortele CC Group R&D Center <w.meeussen.vdmcc at vandemoortele.be>*Date*: Fri, 2 Aug 1996 02:22:41 -0400*Sender*: owner-wri-mathgroup at wolfram.com

hi mathsmen, it may seem silly, but I can't find the expansion factors for decomposing a product of spherical harmonics into a sum of spherical harmonics: Y(a,b) Y(c,d) = Sum[ coefficient[a,b,c,d,l,m=-b-d] Y(l,m=-b-d) ,{l,lower,upper} ] Of course, I can do it (and have) the hard way by explicitly calculating the integrals Integrate[ Y(a,b)Y(c,d) Y(l,m) Sin[th],{th,0,Pi},{fi,0,2Pi}] for all relevant l and m, but that is rather (;-) slow. I hope to do it faster and smarter with the ClebschGordan /or/ ThreeJSymbols. That is however where I got stuck. They seem to work 'the other way round' somehow. Is there anybody out there who can get me unstuck (gets an Aha-Erlebnis reading this) ? The Mma Book is very brief & scanty on pg 561 and 567 as to explaining what these functions do. I can sympatise with Their reason why : it's not the place to give full math courses to the reader. There are other books for that. I know. But don't have them. Do you ? Then give a hand please? Tanx, Wouter. ==== [MESSAGE SEPARATOR] ====