Discrete multiple orthogonal polynomials on shifted lattices

TL;DR

This paper introduces a new class of multiple orthogonal polynomials on shifted integer lattices, providing explicit Rodrigues formulas and detailed analysis for the case of two weights, expanding the theory of discrete orthogonal polynomials.

Contribution

The paper presents a novel class of multiple orthogonal polynomials on shifted lattices with explicit Rodrigues formulas, advancing the understanding of discrete orthogonal polynomial systems.

Findings

Defined a new class of multiple orthogonal polynomials on shifted lattices

Provided explicit Rodrigues formulas for these polynomials

Analyzed the special case of two weights in detail

Abstract

We introduce a new class of polynomials of multiple orthogonality with respect to the product of $r$ classical discrete weights on integer lattices with noninteger shifts. We give explicit representations in the form of the Rodrigues formulas. The case of two weights is described in detail.