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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)