A study of the k-Horn’s hypergeometric function H9,k
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M. S. Metwally1, Lalit Mohan Upadhyaya2, S. Abo-Hasha3 and Karima Hamza4,†
Bull. Pure Appl. Sci. Sect. E Math. Stat.
42E(2), 126–142 (2023)
e-ISSN:2320-3226, Print ISSN:0970-6577
DOI: 10.48165/bpas.2023.42E.2.4
Description
Description
M. S. Metwally1, Lalit Mohan Upadhyaya2, S. Abo-Hasha3 and Karima Hamza4,†
1. Department of Mathematics, Faculty of Science (Suez),
Suez Canal University, Egypt.
2. Department of Mathematics, Municipal Post Graduate College,
Mussoorie, Dehradun, Uttarakhand, India-248179.
3,4. Department of Mathematics, Faculty of Science,
South Valley University, Qena, Egypt.
1. E-mail: met641958@yahoo.com , 2. E-mail: lmupadhyaya@rediffmail.com , hetchres@gmail.com
3. E-mail: dr.shadyhasha@gmail.com , 4. E-mail: karimahamza767@gmail.com
∗ Communicated, edited and typeset in Latex by Jyotindra C. Prajapati (Editor).
Received December 23, 2022 / Revised October 12, 2023 / Accepted October 19, 2023. Online First
Published on December 25, 2023 at https://www.bpasjournals.com/.
†Corresponding author Karima Hamza, E-mail: karimahamza767@gmail.com
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 .
Key words Horn’s hypergeometric H9, the k- Pochhammer symbol, limit formulas, recursion formulas, Upadhyaya transform, Laplace transform, Mellin transform, fractional Fourier transform, double Upadhyaya transform, double Laplace transform, double Mellin transform.
2020 Mathematics Subject Classification 33C45, 33C65, 33C70, 33C20.
