Re: Apparent Documentation Error for SphericalHarmonicY

*To*: mathgroup at smc.vnet.net*Subject*: [mg7889] Re: Apparent Documentation Error for SphericalHarmonicY*From*: schnizer at itp.tu-graz.ac.at (B. Schnizer)*Date*: Thu, 17 Jul 1997 15:35:50 -0400*Organization*: TU-Graz*Sender*: owner-wri-mathgroup at wolfram.com

In article <5ppehb$94a at smc.vnet.net>, BobHanlon at aol.com wrote: > 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 You are completely right, the documentation is wrong. Compare it to Edmonds, Angular Momentum in Quantum Mechanics, Eq.(2.5.29)