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Topic: Legendre Polynomials normalised to Sin[theta]^m
Replies: 13   Last Post: Jul 1, 2013 12:13 PM

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Guido Walter Pettinari

Posts: 29
From: Italy & UK
Registered: 3/24/10
Legendre Polynomials normalised to Sin[theta]^m
Posted: Jun 21, 2013 2:25 PM
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Dear all,

I would be grateful if somebody could point me to a numerical routine (possibly in C) to compute the following special function:

P_lm (cos(theta)) / (sin(theta)^m) ,

where P_lm is an associated Legendre polynomial. The function can be also expresses as

P_lm (x) / (1-x^2)^(m/2) .

Since (1-x^2)^(m/2) is a prefactor in P_lm, I guess that the ratio is even easier to estimate than the P_lm's. I checked in GSL and alglib but alas I could not find this function.

Thank you for your attention,
Guido



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