Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters

TL;DR

This paper introduces new bispectral dual Hahn polynomials that depend on an arbitrary number of continuous parameters, expanding the classical discrete families and their spectral properties.

Contribution

It constructs the first examples of such polynomials with multiple continuous parameters from classical discrete families, using superpositions of Christoffel and Geronimus transforms.

Findings

New bispectral dual Hahn polynomials with arbitrary parameters

Eigenfunctions of higher order difference operators

First such examples from classical discrete families

Abstract

We construct new examples of bispectral dual Hahn polynomials, i.e., orthogonal polynomials with respect to certain superposition of Christoffel and Geronimus transforms of the dual Hahn measure and which are also eigenfunctions of a higher order difference operator. The new examples have the novelty that they depend on an arbitrary number of continuous parameters. These are the first examples with this property constructed from the classical discrete families.