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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Veröffentlicht in:Axioms Jg. 7; H. 2; S. 38
Hauptverfasser: Masjed-Jamei, Mohammad, Koepf, Wolfram
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.06.2018
Schlagworte:
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
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United Kingdom > UK
United States > US
Germany
ISSN:2075-1680, 2075-1680
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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.
AbstractList 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.
Author Koepf, Wolfram
Masjed-Jamei, Mohammad
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  fullname: Koepf, Wolfram
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crossref_primary_10_3390_axioms7040082
crossref_primary_10_3390_math9010074
crossref_primary_10_2989_16073606_2021_1925368
crossref_primary_10_3390_axioms8030087
crossref_primary_10_1186_s13660_018_1888_3
Cites_doi 10.1112/plms/s2-28.1.242
10.1016/j.cam.2009.05.013
10.1007/BFb0060468
10.1007/978-1-4471-6464-7
10.1080/10652460903497259
10.1063/1.1665270
10.1017/CBO9781107325937
10.1007/978-1-4757-1595-8
10.1016/1385-7258(73)90019-X
10.1063/1.1665587
10.1016/S0022-247X(03)00103-3
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Snippet 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...
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StartPage 38
SubjectTerms 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
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