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

[Brian Gough]

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/