Extensions of certain classical summation theorems for the series 2F1, 3F2, and 4F 3 with applications in Ramanujan's summations

Yong Sup Kim, Medhat A. Rakha, Arjun K. Rathie

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24 Citations (Scopus)

Abstract

Motivated by the extension of classical Gauss's summation theorem for the series 2F1 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2F 1, Watson, Dixon and Whipple for the series 3F 2, and a few other hypergeometric identities for the series 3F2 and 4F3. As applications, certain very interesting summations due to Ramanujan have been generalized. The results derived in this paper are simple, interesting, easily established, and may be useful.

Original languageEnglish
Article number309503
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2010
DOIs
Publication statusPublished - 2010

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Ramanujan
Summation
Series
Theorem
Gauss

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

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abstract = "Motivated by the extension of classical Gauss's summation theorem for the series 2F1 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2F 1, Watson, Dixon and Whipple for the series 3F 2, and a few other hypergeometric identities for the series 3F2 and 4F3. As applications, certain very interesting summations due to Ramanujan have been generalized. The results derived in this paper are simple, interesting, easily established, and may be useful.",
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AB - Motivated by the extension of classical Gauss's summation theorem for the series 2F1 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2F 1, Watson, Dixon and Whipple for the series 3F 2, and a few other hypergeometric identities for the series 3F2 and 4F3. As applications, certain very interesting summations due to Ramanujan have been generalized. The results derived in this paper are simple, interesting, easily established, and may be useful.

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