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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