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## Re: [Help-gsl] spherical harmonics for m<0 (m=-l)

**From**: |
Brian Gough |

**Subject**: |
Re: [Help-gsl] spherical harmonics for m<0 (m=-l) |

**Date**: |
Tue, 27 Sep 2005 17:44:21 +0100 |

Drew Parsons writes:
>* I'm working with spherical harmonics, calculated a value for each l*
>* separately by putting together a sum over m of Y_l^m (averaging the*
>* value of the spherical harmonic over a number of neighbouring points in*
>* space) , as in*
>* *
>* \sum_{m=-l}^{l} < Y_l^m (\theta, \phi ) >*
>* *
>* To help get this done GSL offers me gsl_sf_legendre_sphPlm( l, m, x ),*
>* but the function only accepts m >= 0.*
>* *
>* What is the best way to proceed to also count the cases where m < 0 ?*
I think there is a relationship between +m and -m (Abramowitz &Stegun
8.2.5)
If you are computing multiple values you'll want to use the
sphPlm_array function for efficiency.
I'm not sure why the original function is restricted to m>=0, maybe
there was a reason for that.
--
Brian Gough
Network Theory Ltd,
Publishing Free Software Manuals --- http://www.network-theory.co.uk/