MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: 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
> 
Hi Bob,

that is a bug in the documentaion only -- the intern Mathematica definition
of SphericalHarmonicY agrees with the common definiton of the text books and
the normalisation

Integrate[SphericalHarmonicY[l,m,theta,phi]*
          SphericalHarmonicY[l1,m1,theta,phi],{theta,0,Pi},{phi,0,2Pi}]=
          KoneckerDelta[l,l1]*KroneckerDelta[m,m1]
          
Hope that helps
Jens          


  • Prev by Date: Re: character problem
  • Next by Date: Re: Kalman-Filter
  • Previous by thread: Re: Apparent Documentation Error for SphericalHarmonicY
  • Next by thread: Re: Apparent Documentation Error for SphericalHarmonicY