On the ω-multiple Charlier polynomials

Abstract

Abstract The main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice ω N = { 0 , ω , 2 ω , … } $\omega \mathbb{N} = \{ 0,\omega ,2\omega ,\ldots \} $ , ω ∈ R $\omega \in \mathbb{R}$ . 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 ω = 3 2 $\omega =\frac{3}{2}$ and define 3 2 $\frac{3}{2}$ -multiple Charlier polynomials. It is also mentioned that, in the case ω = 1 $\omega =1$ , the obtained results coincide with the existing results of multiple Charlier polynomials.

Keywords

• Multiple orthogonal polynomials
• ω-multiple Charlier polynomials
• Appell polynomials
• Hypergeometric function
• Rodrigues formula
• Generating function