Q-Hermite polynomials and classical orthogonal polynomials

TL;DR

This paper explores the use of generating functions to express orthogonality relations of q-Hermite and classical orthogonal polynomials via q-beta integrals, introducing new orthogonal or biorthogonal systems.

Contribution

It introduces a novel approach to express orthogonality relations using generating functions and q-beta integrals, leading to new sets of orthogonal or biorthogonal polynomials.

Findings

Expressed orthogonality relations through q-beta integrals

Developed new orthogonal or biorthogonal polynomial systems

Provided a framework connecting generating functions with orthogonality

Abstract

We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal