On multiple $\Delta_{\omega}$-Appell polynomials

TL;DR

This paper introduces multiple Δω-polynomials, provides generating functions for multiple Charlier polynomials, and characterizes conditions under which these polynomials are orthogonal, expanding the theoretical framework of polynomial classes.

Contribution

It establishes the notion of multiple Δω-polynomials, derives their key properties, and characterizes when they coincide with multiple Charlier polynomials under orthogonality.

Findings

Generated functions for multiple Charlier polynomials

Characterization of multiple Δω-polynomials

Identification of conditions for orthogonality and equivalence to Charlier polynomials

Abstract

In this paper, we give a generating function for Multiple Charlier polynomials and deduce several consequences for these polynomials as invertion formula, connection formula, addition formula and recurrences relations they satisfy. Next, we introduce the notion of multiple $\Delta_{\omega}$ polynomials and prove several equivalent conditions for this class of polynomials. Also, we give a characterization theorem that if multiple $\Delta_1$ polynomials are also multiple orthogonal, then they are the multiple Charlier polynomials.