• 제목/요약/키워드: Hypergeometric series

검색결과 151건 처리시간 0.022초

SOME PRODUCT FORMULAS OF THE GENERALIZED HYPERGEOMETRIC SERIES

  • Cho, Young-Joon;Seo, Tae-Young;Choi, June-Sang
    • 대한수학회논문집
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    • 제14권4호
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    • pp.843-850
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    • 1999
  • The object of this paper is to give certain classes of pre-sumably new product formulas involving the generalized hypergeo-metric series by modifying the elementary method suggested by Bai-ley.

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A class of infinite series summable by means of fractional calculus

  • Park, June-Sang
    • 대한수학회논문집
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    • 제11권1호
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    • pp.139-145
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    • 1996
  • We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

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SOME FAMILIES OF INFINITE SUMS DERIVED BY MEANS OF FRACTIONAL CALCULUS

  • Romero, Susana Salinas De;Srivastava, H.M.
    • East Asian mathematical journal
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    • 제17권1호
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    • pp.135-146
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    • 2001
  • Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

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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.

Modular Tranformations for Ramanujan's Tenth Order Mock Theta Functions

  • Srivastava, Bhaskar
    • Kyungpook Mathematical Journal
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    • 제45권2호
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    • pp.211-220
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    • 2005
  • In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

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