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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.19 No.2

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INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.2, pp.137-145
https://doi.org/10.7468/jksmeb.2012.19.2.137
Choi, June-Sang
Hasanov, Anvar
Turaev, Mamasali
Choi,, J. , Hasanov,, A. , & Turaev,, M. (2012). INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 137-145, https://doi.org/10.7468/jksmeb.2012.19.2.137

Abstract

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by <TEX>$H_A$</TEX>, <TEX>$H_B$</TEX> and <TEX>$H_C$</TEX>. Each of these three triple hypergeometric functions <TEX>$H_A$</TEX>, <TEX>$H_B$</TEX> and <TEX>$H_C$</TEX> has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function <TEX>$H_B$</TEX>.

keywords
multiple hypergeometric functions, Gauss hypergeometric function <tex> $_2F_1$</tex>, confluent hypergeometric functions, Eulerian integrals, Laplace integrals, Srivastava's triple hypergeometric function <tex> $H_B$</tex>, Exton's functions, Humbert functions, Bessel functions, beta and gamma functions, Appell functions, Picard's integral formula

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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