Support for Gegenbauer polynomials / hyperspherical harmonics?

MikaelSlevinsky / FastTransforms

:bullettrain_front: Fast orthogonal polynomial transforms :surfer:

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Support for Gegenbauer polynomials / hyperspherical harmonics? #82

Open dashstander opened 6 months ago

dashstander commented 6 months ago

Hi! I'm working on problems with data defined on the n-sphere (n >= 128 or so). From looking around the documentation it seems like this library doesn't support that--do I have the right? Are you familiar with any other libraries that support it?

MikaelSlevinsky commented 6 months ago

Hi @dashstander, it only supports spherical harmonics on the 2-sphere.

I'm not sure full hyperspherical harmonic expansions on the 128-sphere are computationally tractable. But if you are looking for just the ultraspherical polynomials themselves, then yes, there are some routines for them here https://github.com/MikaelSlevinsky/FastTransforms/blob/0df512b819db9e17dd14d5eb1beeeafbec4e88bb/src/fasttransforms.h#L72-L80