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