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

Yahya Çin; Nejla Özmen

doi:10.47000/tjmcs.1670975

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

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

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Yahya Çin ^*
0009-0009-9571-6071
Türkiye

Nejla Özmen
0000-0001-7555-1964
Türkiye

Publication Date

December 30, 2025

Submission Date

April 7, 2025

Acceptance Date

July 25, 2025

Published in Issue

Year 2025 Volume: 17 Number: 2

DOI

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

IZ

https://izlik.org/JA82DX48ME

Cite

RIS / Bibtex

APA

Çin, Y., & Özmen, N. (2025). Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials. Turkish Journal of Mathematics and Computer Science, 17(2), 496-511. https://doi.org/10.47000/tjmcs.1670975

AMA

1.Çin Y, Özmen N. Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials. TJMCS. 2025;17(2):496-511. doi:10.47000/tjmcs.1670975

Chicago

Çin, Yahya, and Nejla Özmen. 2025. “Generating Functions and Recurrence Relations for Generalized Two Variable K-Hypergeometric Polynomials”. Turkish Journal of Mathematics and Computer Science 17 (2): 496-511. https://doi.org/10.47000/tjmcs.1670975.

EndNote

Çin Y, Özmen N (December 1, 2025) Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials. Turkish Journal of Mathematics and Computer Science 17 2 496–511.

IEEE

[1]Y. Çin and N. Özmen, “Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials”, TJMCS, vol. 17, no. 2, pp. 496–511, Dec. 2025, doi: 10.47000/tjmcs.1670975.

ISNAD

Çin, Yahya - Özmen, Nejla. “Generating Functions and Recurrence Relations for Generalized Two Variable K-Hypergeometric Polynomials”. Turkish Journal of Mathematics and Computer Science 17/2 (December 1, 2025): 496-511. https://doi.org/10.47000/tjmcs.1670975.

JAMA

1.Çin Y, Özmen N. Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials. TJMCS. 2025;17:496–511.

MLA

Çin, Yahya, and Nejla Özmen. “Generating Functions and Recurrence Relations for Generalized Two Variable K-Hypergeometric Polynomials”. Turkish Journal of Mathematics and Computer Science, vol. 17, no. 2, Dec. 2025, pp. 496-11, doi:10.47000/tjmcs.1670975.

Vancouver

1.Yahya Çin, Nejla Özmen. Generating Functions and Recurrence Relations for Generalized Two Variable k-Hypergeometric Polynomials. TJMCS. 2025 Dec. 1;17(2):496-511. doi:10.47000/tjmcs.1670975