Apparent Documentation Error for SphericalHarmonicY

*To*: mathgroup at smc.vnet.net*Subject*: [mg7764] [mg7764] Apparent Documentation Error for SphericalHarmonicY*From*: BobHanlon at aol.com*Date*: Tue, 8 Jul 1997 14:36:50 -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