Extended Horn’s hypergeometric function $H_{11}$


Extended Horn’s hypergeometric function $H_{11}$

M. S. Metwally1, S. Abo-Hasha2  and Karima Hamza3

BPAS-E-Math and Stat. Vol.42E(1) June 2023

DOI:  10.48165/bpas.2023.42E.1.6

Page: 43-56



Extended Horn’s hypergeometric function $H_{11}$

  1. S. Metwally1, S. Abo-Hasha2 and Karima Hamza3


  1. Department of Mathematics, Faculty of Science (Suez), Suez University, Egypt.

2,3. Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt.

  1. E-mail: met641958@yahoo.com , 2. E-mail: dr.shadyhasha@gmail.com
  2. E-mail: karimahamza767@gmail.com


Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief).

Received October 26, 2022 / Revised April 19, 2023 / Accepted May 04, 2023. Online First Published

on June 30, 2023 at https://www.bpasjournals.com/.


Corresponding author Karima Hamza, E-mail: karimahamza767@gmail.com

In this paper we introduce an extension of the Horn’s hypergeometric function $H_{11}$. Furthermore, we investigate the limit formulas, integral representations, differentiation formulas, infinite sums, recursion formulas, Laplace, Mellin and fractional Fourier transforms for the extended Horn’s hypergeometric function $H_{11}$. Finally, we discuss double Laplace and double Mellin transforms of this function. Key words Horn’s hypergeometric function $H_{11}$, the generalization of the Pochhammer symbol, limit formulas, recursion formulas, Laplace transform, Mellin transform, Fourier transform, Upadhyaya transform.  2020 Mathematics Subject Classification 33C20, 33C45, 33C65, 33C70.