• Title/Summary/Keyword: Generalized Dixon's summation theorem for $_3F_2(1)$

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APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES 2F1

  • Kim, Yong-Sup;Rathie, Arjun K.
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1201-1211
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    • 2009
  • The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series $_3F_2$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Lavoie, Grondin, and Rathie.

ANOTHER PROOF OF CLASSICAL DIXON'S SUMMATION THEOREM FOR THE SERIES 3F2

  • Kim, Insuk;Cho, Myunghyun
    • Honam Mathematical Journal
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    • v.41 no.3
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    • pp.661-666
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    • 2019
  • In this short research note, we aim to provide a new proof of classical Dixon's summation theorem for the series $_3F_2$ with unit argument. The theorem is obtained by evaluating an infinite integral and making use of classical Gauss's and Kummer's summation theorem for the series $_2F_1$.

GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN

  • Song, Hyeong-Kee;Kim, Yong-Sup
    • Honam Mathematical Journal
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    • v.34 no.1
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    • pp.35-44
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    • 2012
  • Motivated by the extension of classical Dixon's summation theorem for the series $_3F_2$ given by Lavoie, Grondin, Rathie and Arora, the authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan.

ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION

  • Lee, Seung Woo;Lee, Chang Hyun;Kim, Yong Sup
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.83-92
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    • 2013
  • The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of $_3F_2$ and the generalized Kummer's theorem for $_2F_1$ obtained earlier by Lavoie et al. [3, 5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON

  • Lee, Seung-Woo;Kim, Yong-Sup
    • Honam Mathematical Journal
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    • v.32 no.1
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    • pp.61-71
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    • 2010
  • The aim of this paper is to extend a number of transformation formulas for the four $X_4$, $X_5$, $X_7$, and $X_8$ among twenty triple hypergeometric series $X_1$ to $X_{20}$ introduced earlier by Exton. The results are derived from the generalized Kummer's theorem and Dixon's theorem obtained earlier by Lavoie et al..

ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS

  • CHOI, JUNE-SANG;RATHIE ARJUN K.;BHOJAK BHARTI
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.169-178
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    • 2005
  • Five results closely related to the well-known Preece's identity obtained earlier by Choi and Rathie will be derived here by using some known hypergeometric identities. In addition to this, the identities obtained earlier by Choi and Rathie have also been written in a compact form.