The para-Racah polynomials

TL;DR

This paper introduces new bispectral orthogonal polynomials on a quadratic bi-lattice derived from Wilson polynomials, providing their recurrence relations, difference equations, and connections to known polynomial families.

Contribution

It presents a novel class of bispectral polynomials obtained via truncation of Wilson polynomials, including explicit formulas and structural properties.

Findings

Orthogonal polynomials on a quadratic bi-lattice are constructed.

Recurrence coefficients are represented by a perturbed persymmetric Jacobi matrix.

Connections to para-Krawtchouk and dual-Hahn polynomials are established.

Abstract

New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed persymmetric Jacobi matrix. The orthogonality relation and an explicit expression in terms of hypergeometric functions are also given. Special cases and connections with the para-Krawtchouk polynomials and the dual-Hahn polynomials are also discussed.