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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.17 No.4

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CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION $X_2$

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X2

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2010, v.17 no.4, pp.347-354
Choi, June-Sang (Department of Mathematics, Dongguk University)
Hasanov, Anvar (Department of Mathematics, Dongguk University)
Turaev, Mamasali (Department of Mathematics, Dongguk University)
Choi, June-Sang, Hasanov, Anvar, & Turaev, Mamasali. (2010). CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION <TEX>$X_2$</TEX>, 17(4), 347-354.

Abstract

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

keywords
generalized hypergeometric series, multiple hypergeometric functions, integrals of Euler type, Laplace integral, Exton functions <tex> $X_i$</tex>, Humbert function <tex> ${\Psi}_2$</tex>, Appell function <tex> $F_4$</tex>, Lauricella function <tex> $F_C$</tex>

참고문헌

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Kim, Yong-Sup;Rathie, Arjun Kumar;Choi, June-Sang. (2009). ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X<SUB>8</SUB>. Communications of the Korean Mathematical Society, 24(4), 517-521. 10.4134/CKMS.2009.24.4.517.

한국수학교육학회지시리즈B:순수및응용수학

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