A study of the k-Horn’s hypergeometric function H9,k∗

M S Metwally; Lalit Mohan Upadhyaya; S Abo-Hasha; Karima Hamza

doi:10.48165/bpas.2023.42E.2.4

Authors

M S Metwally . Department of Mathematics, Faculty of Science (Suez), Suez Canal University, Egypt.
Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India-248179.
S Abo-Hasha Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.
Karima Hamza Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.

DOI:

https://doi.org/10.48165/bpas.2023.42E.2.4

Keywords:

Horn’s hypergeometric H9, the k- Pochhammer symbol, limit formulas, re cursion formulas, Upadhyaya transform, Laplace transform, Mellin transform, fractional Fourier transform, double Upadhyaya transform, double Laplace transform, double Mellin transform

Abstract

In this paper, we introduce the k-Horn’s hypergeometric function H9,k and we investigate its limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, the Laplace, Mellin, fractional Fourier, double Laplace and double Mellin transforms for the k-Horn’s hypergeometric function H9,k. Finally, we discuss the fractional integration and the k-fractional differentiation .

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