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Axioms 2018, 7(2), 38; https://doi.org/10.3390/axioms7020038

Some Summation Theorems for Generalized Hypergeometric Functions

1
Department of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany
2
Department of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, 11369 Tehran, Iran
*
Author to whom correspondence should be addressed.
Received: 2 May 2018 / Revised: 4 June 2018 / Accepted: 6 June 2018 / Published: 8 June 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
Full-Text   |   PDF [253 KB, uploaded 8 June 2018]

Abstract

Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of generalized hypergeometric series in order to extend some classical summation theorems of hypergeometric functions such as Gauss, Kummer, Dixon, Watson, Whipple, Pfaff–Saalschütz and Dougall formulas and also obtain some new summation theorems in the sequel. View Full-Text
Keywords: generalized hypergeometric series; Gauss and confluent hypergeometric functions; classical summation theorems of hypergeometric functions generalized hypergeometric series; Gauss and confluent hypergeometric functions; classical summation theorems of hypergeometric functions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Masjed-Jamei, M.; Koepf, W. Some Summation Theorems for Generalized Hypergeometric Functions. Axioms 2018, 7, 38.

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