Characterization of certain sequences of $q$-polynomials

TL;DR

This paper characterizes specific sequences of quasi-orthogonal polynomials that also form $q$-Appell sets, providing insights into their structure and properties within the framework of $q$-polynomial theory.

Contribution

It introduces a characterization of quasi-orthogonal polynomial sequences that are also $q$-Appell sets, advancing understanding of their dual properties.

Findings

Identifies conditions under which quasi-orthogonal polynomials are $q$-Appell sets

Provides a classification of such polynomial sequences

Enhances theoretical understanding of $q$-polynomial structures

Abstract

A characterization is given of those sequences of quasi-orthogonal polynomials which form also $q$-Appell sets.