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

 From: John Gehman Subject: Re: [Help-gsl] spherical harmonics for m<0 (m=-l) Date: Wed, 28 Sep 2005 09:45:44 +1000

There is a relationship -- look it up for sure, obviously, but I believe the negative values of m are simply the complex conjugate (relevant in the exponential) of the positive m values, and maybe the m = \pm 1 are opposite overall sign to each other.


I hesitated to reply with this earlier, as I presumed that mucking into the functions with this degree of detail to solve the problem defeats the purpose of a simple gsl function, but in light of Brian's reply, perhaps it helps ... ?

Cheers
john

On 28/09/2005, at 2:44 AM, Brian Gough wrote:


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/

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