Introducing the ω - Multiple Meixner Polynomials of the First Kind

Discrete multiple orthogonal polynomials are useful extension of discrete orthogonal polynomials. The theory of discrete orthogonal polynomials on a linear lattice were extended to such polynomials by J. Arvesu, J. Coussement and W. Van Assche. In this study, we introduce a new family of discrete multiple orthogonal polynomials, namely ω-multiple Meixner polynomials of the first kind, where ω is a positive real number. Some structural properties of this family, such as raising operator, Rodrigue’s type formula and explicit representation are derived.The generating function for ω-multiple Meixner polynomials of the first kind is obtained and by use of this generating function we reach to several consequences for these polynomials. One of them is a lowering operator which will be helpful for obtaining a difference equation. We obtain the difference equation which has the ω-multiple Meixner polynomials of first kind as a solution. Also it is shown that for the special case ω = 1, the obtained results coincide with the existing results for multiple Meixner polynomials of the first kind. In the last section as an illustrated example we consider the special case when ω = 1/2 and for the 1/2- multiple Meixner polynomials of the first kind, we state the corresponding result for the main theorems. Overall, this study contributes to the understanding of these polynomial families and provides valuable insights into their properties and applications.