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

Awad, Mohamed M.
Koepf, Wolfram
Mohammed, Asmaa Orabi
Rakha, Medhat Ahmed
Rathie, Arjun Kumar

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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In: Results in Mathematics (RM) Volume 76 / Issue 2 (2021-03-16) , S. ; EISSN 1420-9012
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@article{doi:10.17170/kobra-202103173534,
  author    ={Awad, Mohamed M. and Koepf, Wolfram and Mohammed, Asmaa Orabi and Rakha, Medhat Ahmed and Rathie, Arjun Kumar},
  title    ={A Study of Extensions of Classical Summation Theorems for the Series ₃F₂ and ₄F₃ with Applications},
  keywords ={510 and Hypergeometrische Reihe and Erweiterung and Verallgemeinerung},
  copyright  ={http://creativecommons.org/licenses/by/4.0/},
  language ={en},
  journal  ={Results in Mathematics (RM)},
  year   ={2021-03-16}
}