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

2016/04/17 by J. Arvesú, Arvesú, J., A. M. Ramírez-Aberasturis +1
Mathematics · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1604.04920

openalex publication_date 2016/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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