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