Bivariate Bannai-Ito polynomials

TL;DR

This paper introduces bivariate Bannai-Ito polynomials as a new two-variable extension derived from $q o-1$ limits of existing orthogonal polynomials, with established orthogonality, spectral properties, and recurrence relations.

Contribution

It presents the first two-variable extension of Bannai-Ito polynomials, including their orthogonality, spectral properties, and explicit recurrence relations.

Findings

Polynomials are orthogonal and multispectral.

Diagonalization by Dunkl shift operators demonstrated.

Recurrence relations of 3- and 9-term are provided.

Abstract

A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These new polynomials are also shown to be multispectral. Two Dunkl shift operators are seen to be diagonalized by the bivariate Bannai-Ito polynomials and 3- and 9-term recurrence relations are provided.