Some Summation Theorems for Generalized Hypergeometric Functions

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...

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Bibliographic Details
Published in:Axioms Vol. 7; no. 2; p. 38
Main Authors: Masjed-Jamei, Mohammad, Koepf, Wolfram
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2018
Subjects:
classical summation theorems of hypergeometric functions
Conflicts of interest
Economic models
Gamma function
Gauss and confluent hypergeometric functions
generalized hypergeometric series
Hypergeometric functions
Mathematics
Theorems
New York
United Kingdom > UK
United States > US
Germany
ISSN:2075-1680, 2075-1680
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Summary: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.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms7020038