Toda and Laguerre-Freud equations for multiple discrete orthogonal polynomials with an arbitrary number of weights

TL;DR

This paper extends the theory of multiple discrete orthogonal polynomials by deriving Toda and Laguerre-Freud equations for multiple weights, specifically for generalized Charlier and Meixner II families.

Contribution

It introduces generalized Toda and Laguerre-Freud equations for multiple weights, broadening the understanding of semiclassical multiple discrete orthogonal polynomials.

Findings

Derived multiple Toda equations for generalized Charlier and Meixner II families.

Established Laguerre-Freud equations for these polynomial families.

Extended the framework to an arbitrary number of weights.

Abstract

In this paper, we extend our investigation into semiclassical multiple discrete orthogonal polynomials by considering an arbitrary number of weights. We derive multiple versions of the Toda equations and the Laguerre-Freud equations for the multiple generalized Charlier and multiple generalized Meixner II families.