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CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8
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 Title & Authors
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8
Choi, June-Sang; Hasanov, Anvar; Turaev, Mamasali;
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 Abstract
Exton introduced 20 distinct triple hypergeometric functions whose names are (i = 1, , 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions , , a Humbert function , and a Humbert function . The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function , whose kernels include the Exton functions (, ) itself, the Horn's function , the Gauss hypergeometric function , and Lauricella hypergeometric function . We also provide a system of partial differential equations satisfied by .
 Keywords
generalized hypergeometric series;multiple hypergeometric functions;integrals of Euler type;Laplace integral;Exton functions ;Humbert functions;Appell-Horn function ;Lauricella hypergeometric function ;
 Language
English
 Cited by
 References
1.
P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyperspheriques; Polynomes d'Hermite, Gauthier-Villars, Paris, 1926.

2.
J. Choi, A. K. Rathie, and H. Harsh, Remarks on a summation formula for three variables hypergeometric function $X_{8}$ and certain hypergeometric transformations, East Asian Math. J. 25 (2009), no. 4, 481-486.

3.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.

4.
H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math 4 (1982), no. 2, 113-119.

5.
Y. S. Kim, J. Choi, and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series $X_{8}$, Honam Math. J. 27 (2005), no. 4, 603-608.

6.
Y. S. Kim and A. K. Rathie, On an extension formula for the triple hypergeometric series $X_{8}$ due to Exton, Bull. Korean Math. Soc. 44 (2007), no. 4, 743-751. crossref(new window)

7.
Y. S. Kim, A. K. Rathie, and J. Choi, Another method for Padmanabham's transfor- mation formula for Exton's triple hypergeometric series $X_{8}$, Commun. Korean Math. Soc. 24 (2009), no. 4, 517-521. crossref(new window)

8.
S. W. Lee and Y. S. Kim, An extension of the triple hypergeometric series by Exton, Honam Math. J. 32 (2010), no. 1, 61-71. crossref(new window)

9.
P. A. Padnanabham, Two results on three variable hypergeometric function, Indian J. Pure Appl. Math. 30 (1999), no. 11, 1107-1109.

10.
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), Wiley, New York, Chichester, Brisbane, and Toronto, 1985.