On the orthogonality of q-classical polynomials of the Hahn class II

TL;DR

This paper investigates the orthogonality properties of various $q$-polynomials in the Hahn class, extending previous work and establishing new orthogonality relations, including for the $q$-Meixner polynomials.

Contribution

It advances the understanding of orthogonality in $q$-classical polynomials of the Hahn class by analyzing multiple cases and deriving new relations, notably for the $q$-Meixner polynomials.

Findings

New orthogonality relation for $q$-Meixner polynomials

Extended analysis of orthogonality in multiple $q$-polynomial cases

Progress in understanding $q$-polynomials of the Hahn class

Abstract

In this article, the study of the orthogonality properties of $q$-polynomials of the Hahn class started in the initial article by R. \'Alvarez-Nodarse, R. Sevinik-Ad{\i}g\"uzel, and H. Ta\c{s}eli, \textit{On the orthogonality of $q$-classical polynomials of the Hahn class I} is proceeded. To be more specific, the orthogonality properties of the $q$-polynomials belonging to the $\emptyset$-Hermite-Laguerre/Jacobi, $\emptyset$-Jacobi/Hermite-Laguerre, 0-Laguerre/Jacobi-Bessel and 0-Jacobi/Laguerre-Bessel cases are studied by taking into account the idea considered in the initial paper. In particular, a new orthogonality relation for the $q$-Meixner polynomials is established.