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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
Re: Legendre Polynomials normalised to Sin[theta]^m
Posted: Jun 22, 2013 10:00 AM
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I would like to add that, since I need to evaluate this function very close to theta=n*pi, I cannot just use the result from a Legendre polynomial routine and divide it by sin(theta)^m.

Thanks,
Guido



Il giorno venerdì 21 giugno 2013 20:25:51 UTC+2, Guido Walter Pettinari ha scritto:
> Dear all,
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> I would be grateful if somebody could point me to a numerical routine (possibly in C) to compute the following special function:
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> P_lm (cos(theta)) / (sin(theta)^m) ,
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> where P_lm is an associated Legendre polynomial. The function can be also expresses as
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> P_lm (x) / (1-x^2)^(m/2) .
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> 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.
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> Thank you for your attention,
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> Guido





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