Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials

Year 2025, Volume: 17 Issue: 2, 496 - 511, 30.12.2025

Yahya Çin , Nejla Özmen

https://doi.org/10.47000/tjmcs.1670975

Abstract

In this paper, we present the sum expressions and generating function
relations for the generalized $k$-hypergeometric polynomials in two
variables. The methods used here are inspired by previous works, such as
those found in [21, 23, 24]. We establish several
theorems and demonstrate their applications for the generalized two-variable
$k$-hypergeometric polynomials, providing their integral representation.
Furthermore, we explore various recurrence relations for the generalized
polynomials $I_{n,k}\left( \alpha ;\beta ;x,y\right) $, as discussed in
references (3.2) and (3.4). The results presented are expected to
contribute to the further understanding and application of these polynomials
in mathematical and applied contexts.

Keywords

gamma and beta k-function , generalized two variable k−hypergeometric polynomials , generating function , multilinear and multilateral generating functions , integral representation , recurrence relations

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