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Ridge polynomials (on the disk)? #89

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MikaelSlevinsky opened this issue Jun 4, 2021 · 2 comments
Open

Ridge polynomials (on the disk)? #89

MikaelSlevinsky opened this issue Jun 4, 2021 · 2 comments

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@MikaelSlevinsky
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MikaelSlevinsky commented Jun 4, 2021 •
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These look like P_{n,k}(x,y) = U_n(x * cos(k*pi/(n+1)) + y * sin(k*pi/(n+1))), orthogonal on the unweighted unit disk.

Sparse differentiation is trivial (using ultraspherical generalizations), but the Jacobi operators are not obvious.
@MikaelSlevinsky
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https://www.math.auckland.ac.nz/~waldron/Preprints/Disc-Polys/discpolys.pdf

@dlfivefifty
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Yes I know this family from Dunkl and Xu, it’s cool and doesn’t require any high order OPs

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@dlfivefifty @MikaelSlevinsky