On the ω -multiple Charlier polynomials

Advances in Difference Equations

article

Özarslan, Mehmet Ali¹  Baran, Gizem¹ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University

关键词: Multiple orthogonal polynomials;    ω -multiple Charlier polynomials;    Appell polynomials;    Hypergeometric function;    Rodrigues formula;    Generating function;    Difference equation;   

DOI  :  10.1186/s13662-021-03278-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The 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 \} $ ,$\omega \in \mathbb{R}$ . 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$( r+1 )$ th order difference equation is given. As an example we consider the case$\omega =\frac{3}{2}$ and define$\frac{3}{2}$ -multiple Charlier polynomials. It is also mentioned that, in the case$\omega =1$ , the obtained results coincide with the existing results of multiple Charlier polynomials.

【 授权许可】

CC BY