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An algebraic treatment of the Askey biorthogonal polynomials on the unit circle

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arxiv 2102.01779 v1 pith:OMFXD5SI submitted 2021-02-02 math.RT

Luc Vinet , Alexei Zhedanov This is my paper · ORCID
classification math.RT
keywords polynomialsalgebraalgebraicaskeybiorthogonalcircleunitbispectral
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abstract

A joint algebraic interpretation of the biorthogonal Askey polynomials on the unit circle and of the orthogonal Jacobi polynomials is offered. It ties their bispectral properties to an algebra called the meta-Jacobi algebra $m\mathfrak{J}$.

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  1. Bispectrality of the sieved Jacobi polynomials

    math.CA 2025-01 conditional novelty 8.0 of 10

    The sieved Jacobi polynomials are shown to be eigenfunctions of new Dunkl-type differential operators, so they are bispectral.

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