• 제목/요약/키워드: Dixon's summation theorem for $_3F_2(1)$

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

  • Kim, Insuk;Cho, Myunghyun
    • 호남수학학술지
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    • 제41권3호
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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 $_2F_1$.

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

  • Kim, Yong-Sup;Rathie, Arjun K.
    • 대한수학회보
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    • 제46권6호
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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 GENERALIZATION OF A RAMANUJAN SUMMATION

  • Lee, Seung Woo;Lee, Chang Hyun;Kim, Yong Sup
    • 호남수학학술지
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    • 제35권1호
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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.

GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN

  • Song, Hyeong-Kee;Kim, Yong-Sup
    • 호남수학학술지
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    • 제34권1호
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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.

AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON

  • Lee, Seung-Woo;Kim, Yong-Sup
    • 호남수학학술지
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    • 제32권1호
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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..