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MathGroup Archive 1997

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Re: Apparent Documentation Error for SphericalHarmonicY

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7804] Re: [mg7764] Apparent Documentation Error for SphericalHarmonicY
  • From: jpk at max.mpae.gwdg.de
  • Date: Sat, 12 Jul 1997 02:45:48 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> SphericalHarmonicY[n, m, theta, phi] // FunctionExpand
> 
> includes a factor of 
> 
>      Sqrt[Gamma[n-m+1]/Gamma[n+m+1]] 
> 
> whereas the on-line documentation and the Mathematica Reference Guide reflect
> the reciprocal factor, i.e.,
> 
>      Sqrt[(n+m)!/(n-m)!]
> 
> Assuming that the implementation was checked more rigorously than the
> documentation, the documentation needs to be corrected.  
> 
> Note:  The Hypergeometric2F1 which occurs in the FunctionExpand is
> expressible as the associated Legendre polynomial (LegendreP) reflected in
> the documentation -- the only difference being that identified above.
> 
> 
> Bob Hanlon
> 
Hi Bob,

that is a bug in the documentaion only -- the intern Mathematica definition
of SphericalHarmonicY agrees with the common definiton of the text books and
the normalisation

Integrate[SphericalHarmonicY[l,m,theta,phi]*
          SphericalHarmonicY[l1,m1,theta,phi],{theta,0,Pi},{phi,0,2Pi}]=
          KoneckerDelta[l,l1]*KroneckerDelta[m,m1]
          
Hope that helps
Jens          


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