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

TL;DR

This paper provides an algebraic framework connecting Askey biorthogonal polynomials on the unit circle with Jacobi polynomials, revealing their bispectral properties through the meta-Jacobi algebra.

Contribution

It introduces a joint algebraic interpretation that unifies the properties of these polynomials via the meta-Jacobi algebra.

Findings

Algebraic interpretation of Askey and Jacobi polynomials

Connection between bispectral properties and meta-Jacobi algebra

Unified framework for biorthogonal and orthogonal polynomials

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 $m\mathfrak{J}$.