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MathGroup Archive 1996

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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.


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