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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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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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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References_xml	– volume: 2 start-page: 242 year: 1928 ident: ref_7 article-title: Products of generalized hypergeometric series publication-title: Proc. Lond. Math. Soc. doi: 10.1112/plms/s2-28.1.242 – volume: 231 start-page: 964 year: 2009 ident: ref_9 article-title: Certain summation and transformation formulas for generalized hypergeometric series publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2009.05.013 – ident: ref_5 doi: 10.1007/BFb0060468 – ident: ref_1 doi: 10.1007/978-1-4471-6464-7 – ident: ref_4 – volume: 21 start-page: 603 year: 2010 ident: ref_10 article-title: Karlsson-Minton summation theorems for the generalized hypergeometric series of unit argument publication-title: Integral Transform. Spec. Funct. doi: 10.1080/10652460903497259 – ident: ref_2 – volume: 11 start-page: 1375 year: 1970 ident: ref_11 article-title: Generalized hypergeometric function of unit argument publication-title: J. Math. Phys. doi: 10.1063/1.1665270 – ident: ref_3 doi: 10.1017/CBO9781107325937 – ident: ref_14 – ident: ref_6 doi: 10.1007/978-1-4757-1595-8 – volume: 76 start-page: 38 year: 1973 ident: ref_13 article-title: Generalized hypergeometric functions with integral parameter differences publication-title: Indag. Math. doi: 10.1016/1385-7258(73)90019-X – volume: 12 start-page: 270 year: 1971 ident: ref_8 article-title: Hypergeometric functions with integral parameter differences publication-title: J. Math. Phys. doi: 10.1063/1.1665587 – volume: 281 start-page: 332 year: 2003 ident: ref_12 article-title: Karlsson-Minton type hypergeometric functions on the root system Cn publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(03)00103-3
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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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Title	Some Summation Theorems for Generalized Hypergeometric Functions
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