CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X2

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

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>. 한국수학교육학회지시리즈B:순수및응용수학, 17(4), 347-354.

복사

Abstract

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

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.

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Vol.17 No.4

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION <TEX>$X_2$</TEX>

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X2

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학