On some Algebraic Properties for q-Meixner Multiple Orthogonal Polynomials of the First Kind

TL;DR

This paper introduces a new family of q-Meixner multiple orthogonal polynomials of the first kind, exploring their algebraic properties, difference equations, and recurrence relations within a non-uniform lattice framework.

Contribution

It provides explicit algebraic operators, difference equations, and recurrence relations for the q-Meixner multiple orthogonal polynomials of the first kind, expanding the understanding of their structure.

Findings

Derived high-order linear q-difference equation with polynomial coefficients.

Established raising and lowering operators for the polynomials.

Obtained the nearest neighbor recurrence relation algebraically.

Abstract

We study a new family of q-Meixner multiple orthogonal polynomials of the first kind. The discrete orthogonality conditions are considered over a non-uniform lattice with respect to different q-analogues of Pascal distributions. We address some algebraic properties, namely raising and lowering operators as well as Rodrigues-type. Based on the explicit expressions for the raising and lowering operator a high-order linear q-difference equation with polynomial coefficients for the q-Meixner multiple orthogonal polynomials of the first kind is obtained. Finally, we obtain the nearest neighbor recurrence relation based on a purely algebraic approach.