Associated Legendre polynomials are requested

[feima0011]

Associated Legendre polynomials are requested
https://en.wikipedia.org/wiki/Associated_Legendre_polynomials

[ludoro]

I would love to try and implement these! Working on it.

[simonbyrne]

@feima0011 Can you expand on how you're using them? i.e. are you evaluating the same polynomial multiple times? If so, is it on a grid?

[feima0011]

@feima0011 Can you expand on how you're using them? i.e. are you evaluating the same polynomial multiple times? If so, is it on a grid?

I am working on the acoustic wave equations. I need the Associated Legendre polynomials
to calculate the spherical harmonics. I have to calculate the value of the Associated Legendre polynomials multiple times, and they are on a grid.

[simonbyrne]

Do you have a link to code where they are used?

[feima0011]

Currently, i am using the GSL.jl library to calculate the Associated Legendre polynomials .
The following library have code for calculate the Associated Legendre polynomials, but it is outdated.
https://github.com/milthorpe/SphericalHarmonics.jl

[MikaelSlevinsky]

Have you tried using the spherical harmonica transforms in FastTransforms.jl? There is an example on usage here https://github.com/MikaelSlevinsky/FastTransforms.jl/blob/master/examples/sphere.jl

[feima0011]

Hi Richard Mikael Slevinsky : I have heard that package before. I think a standalone code to compute the Legendre polynomial is better than the code in that package. fei

…

On Fri, Dec 28, 2018 at 2:56 PM Richard Mikael Slevinsky < ***@***.***> wrote: Have you tried using the spherical harmonica transforms in FastTransforms.jl? There is an example on usage here https://github.com/MikaelSlevinsky/FastTransforms.jl/blob/master/examples/sphere.jl — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#124 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AVmmpYxsgsAQI9V0UufjbpO78DNu3NFUks5u9ZZ_gaJpZM4XFCOL> .

[arturgower]

I agree with Fei. Associated Legendre polynomials, and spherical harmonics, are core to so many branches of physics. They involve many connections to other special functions and complicated identities. It makes sense to have them embedded in SpecialFunctions.jl.

[PaulXiCao]

We could start at Legendre Polynomials, then Associated Legendre Polynomials and then Spherical Harmonics?

Concerning Legendre Polynomials
We should implement a standard method using the recurrenc relation which is alright for small orders.
For higher orders I found a paper which describes an algorithm to compute Legendre Polynomials in constant time by precomputation. It is quite involved. I am not sure if we should include that in SpecialFunctions. Maybe a standalone package is better?

[PaulXiCao]

The associated Legendre polynomials (functions of first kind) have been implemented by a simple recursion formula in pr #175 (one of the later commits).

[LeoGalPras]

Should this be merged with issues #175 and #177 ???