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.
Author(s) Details:
Sonuç Zorlu Ogurlu,
Department of Mathematics, Eastern Mediterranean University,
Famagusta, North Cyprus via Mersin 10, Turkey.
Ilkay
Elidemir,
Department
of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus via
Mersin 10, Turkey.
Please see the link here: https://stm.bookpi.org/RUMCS-V5/article/view/14214
