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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 29, 2013 9:23 AM

Dear mecej4,

Thank you for your interest in this issue. I need to compute the function

P_l^m (x)/(1-x^2)^(m/2)

for values of |1-x| that can be as small as 10^-7 and in (roughly) the following ranges of l and m:
0 < l <100
-10 < m < 10.

In the worst case I could write down the polynomials explicitly in the C code, but I would rather avoid doing that. In any case, this is the Mathematica code to generate the polynomials:
With[{l = 5, m = 2},
LegendreP[l, m, x]/(1 - x^2)^(m/2)
] // Simplify

Thanks,
Guido

Il giorno sabato 29 giugno 2013 14:43:44 UTC+2, mecej4 ha scritto:
> If you can be more specific, i.e., state what values of l and m are of
>
> interest to you, it may be possible to find a solution.
>
>
>
> Some of the problems that you mentioned in this thread are artifacts of
>
> the re-parametrization in terms of x = cos \theta. The expressions for
>
> P_l^m (x)/(1-x^2)^(m/2) are simple polynomials in x.
>
>
>
> -- mecej4

Date Subject Author
6/21/13 Guido Walter Pettinari
6/22/13 Guido Walter Pettinari
6/22/13 AMX
6/24/13 Mike Trainor
6/26/13 AMX
6/29/13 Guido Walter Pettinari
6/23/13 Waldek Hebisch
6/29/13 Guido Walter Pettinari
6/29/13 mecej4
6/29/13 Guido Walter Pettinari
6/29/13 mecej4
6/29/13 Guido Walter Pettinari
7/1/13 Wolfgang Ehrhardt
7/1/13 Guido Walter Pettinari