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