Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials
Year: 2025
Type: article
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.
Authors: Yahya Çin, Nejla Özmen
Institution: Düzce Üniversitesi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7117595931