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product of Spher.Harmonics
Posted:
Jul 28, 1996 11:19 PM


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=bd] Y(l,m=bd) ,{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 AhaErlebnis 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.



