MathGroup Archive 1997

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Apparent Documentation Error for SphericalHarmonicY


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


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