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http://dx.doi.org/10.5831/HMJ.2012.34.4.473

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HC  

Choi, Junesang (Department of Mathematics, Dongguk University)
Hasanov, Anvar (Department of Mathematics, I. M. Gubkin Russian State University of Oil and Gas)
Turaev, Mamasali (Department of Mathematics, Dongguk University)
Publication Information
Honam Mathematical Journal / v.34, no.4, 2012 , pp. 473-482 More about this Journal
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 hypergeo-metric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ 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 $H_C$.
Keywords
Multiple hypergeometric functions; Gauss hypergeometric function $_2F_1$; Confluent hypergeometric functions; Eulerian integrals; Laplace integrals; Srivastava's triple hypergeometric function $H_C$; Exton's functions; Humbert functions; Bessel functions; Beta and Gamma functions; Appell functions; Picard's integral formula;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper- spheriques; Polynomes d'Hermite, Gauthier - Villars, Paris, 1926.
2 J. Choi, A. Hasanov, H. M. Srivastava and M. Turaev, Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math. 15 (2011), 2751-2762.   DOI
3 J. Choi, A. Hasanov and M. Turaev, Integral representations for Srivastava's triple hypergeometric function HA, Honam Math. J. 34 (2012), 113-124.   DOI   ScienceOn
4 J. Choi, A. Hasanov and M. Turaev, Integral representations for Srivastava's triple hypergeometric function HB, J. Korean Soc. Math. Edu. Series B: Pure Appl. Math. 19(2) (2012), 137-145.
5 G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ. Mat. Palermo 7 (1893), 111-158.   DOI
6 A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcen- dental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
7 H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113-119.
8 A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F\frac{(r)}{A}$ and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), 113-121.   DOI   ScienceOn
9 A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Comput. Math. Appl. 53 (2007), 1119-1128.   DOI   ScienceOn
10 A. Hasanov, H. M. Srivastava and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), 955-969.   DOI   ScienceOn
11 M. Turaev, Decomposition formulas for Srivastava's hypergeometric function $H_{A}$on Saran functions, J. Comput. Appl. Math. 233 (2009), 842-846.   DOI   ScienceOn
12 P. A. Padnanabham, Two results on three variable hypergeometric function, Indian J. Pure Appl. Math. 30 (1999), 1107-1109.
13 S. Saran, Hypergeometric functions of three variables, Ganita 5 (1954), 71-91.
14 H. M. Srivastava, Hypergeometric functions of three variables, Ganita 15 (1964), 97-108.
15 H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo 16 (1967), 99-115.   DOI
16 H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
17 H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
18 H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
19 H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.