Some Appell-type orthogonal polynomials on lattices

TL;DR

This paper explores Appel-type orthogonal polynomials on q-quadratic lattices, providing new characterizations of Al-Salam Chihara and Rogers q-Hermite polynomials, with methods applicable to broader classes of lattice polynomials.

Contribution

It introduces novel characterization theorems for classical and semiclassical orthogonal polynomials on lattices using new analytical methods.

Findings

New characterizations of Al-Salam Chihara polynomials

Descriptions of Rogers q-Hermite polynomials

Method applicability to Askey-Wilson and averaging operators

Abstract

We investigate on some Appel-type orthogonal polynomial sequences on q-quadratic lattices and we provide some entire new characterizations of the Al-Salam Chihara polynomials (including the Rogers q-Hermite polynomials). The corresponding forms are well described. The proposed method can be applied to similar and to more general problems involving the Askey-Wilson and the Averaging operators, in order to obtain new characterization theorems for classical and semiclassical orthogonal polynomials on lattices.