A Study of Extensions of Classical Summation Theorems for the Series 3F2 and 4F3 with Applications

Mohamed M. Awad; Wolfram Koepf; Asmaa O. Mohammed; Medhat A. Rakha; Arjun K. Rathie

doi:10.1007/s00025-021-01367-9

A Study of Extensions of Classical Summation Theorems for the Series ₃F₂ and ₄F₃ with Applications

Mohamed M. Awad, Wolfram Koepf^*, Asmaa O. Mohammed, Medhat A. Rakha, Arjun K. Rathie

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Very recently, Masjed-Jamei & Koepf [Some summation theorems for generalized hypergeometric functions, Axioms, 2018, 7, 38, 10.3390/axioms 7020038] established some summation theorems for the generalized hypergeometric functions. The aim of this paper is to establish extensions of some of their summation theorems in the most general form. As an application, several Eulerian-type and Laplace-type integrals have also been given. Results earlier obtained by Jun et al. and Koepf et al. follow special cases of our main findings.

Original language	English
Article number	65
Journal	Results in Mathematics
Volume	76
Issue number	2
DOIs	https://doi.org/10.1007/s00025-021-01367-9
Publication status	Published - May 2021

Keywords

Generalized hypergeometric function
classical summation theorems
generalizations and extensions

ASJC Scopus subject areas

Mathematics (miscellaneous)
Applied Mathematics

Access to Document

10.1007/s00025-021-01367-9

Cite this

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title = "A Study of Extensions of Classical Summation Theorems for the Series 3F2 and 4F3 with Applications",

abstract = "Very recently, Masjed-Jamei & Koepf [Some summation theorems for generalized hypergeometric functions, Axioms, 2018, 7, 38, 10.3390/axioms 7020038] established some summation theorems for the generalized hypergeometric functions. The aim of this paper is to establish extensions of some of their summation theorems in the most general form. As an application, several Eulerian-type and Laplace-type integrals have also been given. Results earlier obtained by Jun et al. and Koepf et al. follow special cases of our main findings.",

keywords = "Generalized hypergeometric function, classical summation theorems, generalizations and extensions",

author = "Awad, {Mohamed M.} and Wolfram Koepf and Mohammed, {Asmaa O.} and Rakha, {Medhat A.} and Rathie, {Arjun K.}",

note = "Funding Information: Open Access funding enabled and organized by Projekt DEAL. The third and the fourth authors were supported financially by the Academy of Scientific Research and Technology (ASRT), Egypt, Science UP Grant No. 6491. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

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AU - Awad, Mohamed M.

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AU - Mohammed, Asmaa O.

AU - Rakha, Medhat A.

AU - Rathie, Arjun K.

N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. The third and the fourth authors were supported financially by the Academy of Scientific Research and Technology (ASRT), Egypt, Science UP Grant No. 6491. Publisher Copyright: © 2021, The Author(s).

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AB - Very recently, Masjed-Jamei & Koepf [Some summation theorems for generalized hypergeometric functions, Axioms, 2018, 7, 38, 10.3390/axioms 7020038] established some summation theorems for the generalized hypergeometric functions. The aim of this paper is to establish extensions of some of their summation theorems in the most general form. As an application, several Eulerian-type and Laplace-type integrals have also been given. Results earlier obtained by Jun et al. and Koepf et al. follow special cases of our main findings.

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