Re: Apparent Documentation Error for SphericalHarmonicY
- To: mathgroup at smc.vnet.net
- Subject: [mg7801] Re: Apparent Documentation Error for SphericalHarmonicY
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 8 Jul 1997 22:41:13 -0400
- Organization: University of Western Australia
- Sender: owner-wri-mathgroup at wolfram.com
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.
You are correct and the documentation is incorrect as the following
Notebook shows:
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Cell[BoxData[
\(TraditionalForm
\`\(Y\_l\%m\)(\[Theta], \[Phi]) =
\(\ at \(\((2 l + 1)\)/\((4 \[Pi])\)\)\)
\(\ at \(\(\((l + m)\)!\)/\(\((l - m)\)!\)\)\)
\(\(P\_l\%m\)(cos(\[Theta]))\) e\^\(i m \[Phi]\)\)],
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" where ",
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(which agrees with Angular Momentum in Quantum Mechanics by Edmonds \
apart from a phase factor) as can be seen from\
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Cell[BoxData[
\(TraditionalForm\`\[Theta]\ \[Epsilon]\ [0, \[Pi]]\)]],
"."
}], "Text"]
}
]
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA 6907 mailto:paul at physics.uwa.edu.au
AUSTRALIA http://www.pd.uwa.edu.au/Paul
God IS a weakly left-handed dice player
____________________________________________________________________