Discrete orthogonality of hypergeometric polynomial sequences on linear and quadratic lattices

TL;DR

This paper introduces a method to find weight functions for discrete orthogonality of certain hypergeometric polynomial sequences on linear and quadratic lattices, expanding the understanding of orthogonal polynomials in the Askey scheme.

Contribution

It provides a novel approach to determine weight functions for discrete orthogonality, excluding classical polynomials like Jacobi, Bessel, Laguerre, and Hermite.

Findings

Derived weight functions for hypergeometric polynomial sequences on lattices

Established discrete orthogonality conditions for a broad class of polynomials

Extended the framework of orthogonal polynomials beyond classical cases

Abstract

We present a method to obtain weight functions associated with linear and quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional of the orthogonal polynomial sequences in the Askey scheme, with the exception of the Jacobi, Bessel, Laguerre, and Hermite polynomials.