Pearson Equations for Discrete Orthogonal Polynomials: III. Christoffel and Geronimus transformations

TL;DR

This paper explores how Christoffel and Geronimus transformations relate to hypergeometric relations in semiclassical discrete orthogonal polynomials, providing explicit formulas for shifted polynomials.

Contribution

It introduces quasi-determinantal expressions for shifted semiclassical discrete orthogonal polynomials via Christoffel-Geronimus-Uvarov formulas.

Findings

Derived explicit formulas for shifted polynomials

Connected hypergeometric relations with transformation techniques

Enhanced understanding of semiclassical discrete orthogonal polynomials

Abstract

Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are described as Christoffel and Geronimus transformations. Using the Christoffel-Geronimus-Uvarov formulas quasi-determinatal expressions for the shifted semiclassical discrete orthogonal polynomials are obtained.