• Title/Summary/Keyword: Triple hypergeometric series $X_8$

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ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X8 DUE TO EXTON

  • Kim, Yong-Sup;Rathie, Arjun K.
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.743-751
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    • 2007
  • The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X8

  • Kim, Yong-Sup;Rathie, Arjun Kumar;Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.24 no.4
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    • pp.517-521
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    • 2009
  • The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$ by using a different method from that of Padmanabham's. An interesting special case is also pointed out.

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..

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • Communications of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.257-264
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    • 2012
  • Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

REMARKS ON A SUMMATION FORMULA FOR THREE-VARIABLES HYPERGEOMETRIC FUNCTION $X_8$ AND CERTAIN HYPERGEOMETRIC TRANSFORMATIONS

  • Choi, June-Sang;Rathie, Arjun K.;Harsh, H.
    • East Asian mathematical journal
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    • v.25 no.4
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    • pp.481-486
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    • 2009
  • The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function $X_8$ introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.