ON (K, P, S)-GENERALIZATIONS OF THE GAMMA, BETA AND HYPERGEOMETRIC FUNCTIONS AND THEIR PROPERTIES

Maisoon Ahmed Kulaib; Ahmed Ali Atash

doi:10.47372/ejua-ba.2026.1.494

ON (K, P, S)-GENERALIZATIONS OF THE GAMMA, BETA AND HYPERGEOMETRIC FUNCTIONS AND THEIR PROPERTIES

Authors

Maisoon Ahmed Kulaib Dept. of Basic Sciences (Mathematics), Faculty of Engineering, University of Aden, Aden, Yemen
Ahmed Ali Atash Dept. of Mathematics, Faculty of Education, Shabwah University, Shabwah, Yemen

DOI:

https://doi.org/10.47372/ejua-ba.2026.1.494

Keywords:

(k-p-s)-Pochhammer's symbol, (k-p-s)-Gamma function, (k-p-s)- beta functions, (k p s) generalized hypergeometric function, Integral representations

Abstract

In this paper, we introduce a unified three-parameter ((k,p,s))-generalization of the Pochhammer symbol, Gamma and Beta functions. Based on these definitions, a corresponding ((k,p,s))-generalized hypergeometric function is defined. Several fundamental properties are derived, including functional equations, summation formulas and integral representations. It is shown that many known extensions of special functions arise as particular cases of the proposed framework, thereby unifying and extending earlier results in the literature.

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Published

2026-03-31

How to Cite

Kulaib, M. A., & Atash, A. A. (2026). ON (K, P, S)-GENERALIZATIONS OF THE GAMMA, BETA AND HYPERGEOMETRIC FUNCTIONS AND THEIR PROPERTIES. Electronic Journal of University of Aden for Basic and Applied Sciences, 7(1), 9–17. https://doi.org/10.47372/ejua-ba.2026.1.494