On the ω-multiple Charlier polynomials

Abstract

AbstractThe main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice $\omega \mathbb{N} = \{ 0,\omega ,2\omega ,\ldots \} $ ω N = { 0 , ω , 2 ω , … } , $\omega \in \mathbb{R}$ ω ∈ R . We call these polynomials ω-multiple Charlier polynomials. Some of their properties, such as the raising operator, the Rodrigues formula, an explicit representation and a generating function are obtained. Also an $( r+1 )$ ( r + 1 ) th order difference equation is given. As an example we consider the case $\omega =\frac{3}{2}$ ω = 3 2 and define $\frac{3}{2}$ 3 2 -multiple Charlier polynomials. It is also mentioned that, in the case $\omega =1$ ω = 1 , the obtained results coincide with the existing results of multiple Charlier polynomials.