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MikaelSlevinsky / FastTransforms

:bullettrain_front: Fast orthogonal polynomial transforms :surfer:
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Two parameter rectangularized disk polynomials #68

Open MikaelSlevinsky opened 3 years ago

MikaelSlevinsky commented 3 years ago

Dunkl-Xu polynomials with the weight (1-x^2-y^2)^β are written in terms of equal-parameter Jacobi polynomials. These can be generalized in two ways: with inequal-parameter Jacobi polynomials for a weight like (1-sqrt(x^2+y^2))^α(1+sqrt(x^2+y^2))^β; or with equal-parameter Jacobi polynomials with the quadratic transformations for a weight like (x^2+y^2)^α(1-x^2-y^2)^β. The latter, which I prefer due to their correspondence with generalized Zernike, are like 2D Konoplev OPs with a symmetric weight on [-1,1] with interior algebraic factor. @dlfivefifty

dlfivefifty commented 3 years ago

I don't think have a use for the α term at this point. I was hoping at some point to use α for Coulomb potentials but that's been delayed.

so I don't have any strong opinions but agree that the latter is more natural