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