Taiwanese Journal of Mathematics

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA’S TRIPLE HYPERGEOMETRIC FUNCTIONS

Junesang Choi, Anvar Hasanov, H. M. Srivastava, and Mamasali Turaev

Full-text: Open access

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 $H_A$, $H_B$ 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 each of Srivastava's triple hypergeometric functions $H_A$, $H_B$ and $H_C$.

Article information

Source
Taiwanese J. Math., Volume 15, Number 6 (2011), 2751-2762.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406495

Digital Object Identifier
doi:10.11650/twjm/1500406495

Mathematical Reviews number (MathSciNet)
MR2896142

Zentralblatt MATH identifier
1250.33009

Subjects
Primary: 33C20: Generalized hypergeometric series, $_pF_q$ 33C65: Appell, Horn and Lauricella functions
Secondary: 33C05: Classical hypergeometric functions, $_2F_1$ 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions) 33C70: Other hypergeometric functions and integrals in several variables 68Q40 11Y35: Analytic computations

Keywords
multiple hypergeometric functions Gauss hypergeometric function ${}_2F_1$ confluent hypergeometric functions Eulerian integrals Laplace integrals Srivastava's triple hypergeometric functions $H_A$ $H_B$ and $H_C$ Exton's functions

Citation

Choi, Junesang; Hasanov, Anvar; Srivastava, H. M.; Turaev, Mamasali. INTEGRAL REPRESENTATIONS FOR SRIVASTAVA’S TRIPLE HYPERGEOMETRIC FUNCTIONS. Taiwanese J. Math. 15 (2011), no. 6, 2751--2762. doi:10.11650/twjm/1500406495. https://projecteuclid.org/euclid.twjm/1500406495


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References

  • P. Appell and J. Kampé de Fériet, Fonctions Hypergéométriques et Hypersphériques; Polynômes d'Hermite, Gauthier-Villars, Paris, 1926.
  • A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
  • H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math., 4 (1982), 113-119.
  • A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F_A^{\left( r \right)} $ and other multiple hypergeometric functions, Appl. Math. Lett., 19 (2006), 113-121.
  • A. Hasanov and H. M. Srivastava, Decomposition formulas associated with theLauricella multivariable hypergeometric functions, Comput. Math. Appl., 53 (2007), 1119-1128.
  • A. Hasanov, H. M. Srivastava and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl., 324 (2006), 955-969.
  • G. Lauricella, Sulle funzioni ipergeometriche a più variabili, Rend. Circ. Mat. Palermo, 7 (1893), 111-158.
  • P. A. Padmanabham, Two results on three variable hypergeometric function, Indian J. Pure Appl. Math., 30 (1999), 1107-1109. \def\uudnn\raisebox-0.85ex\large $\cdot $
  • S. Saran, Hypergeometric functions of three variables, Ga\uudnita, 5 (1954), 71-91; see also Corrigendum, Ga\dnita, 7 (1956), 65.
  • H. M. Srivastava, Hypergeometric functions of three variables, Ga\uudnita, 15 (1964), 97-108.
  • H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo $($Ser. $2)$, 16 (1967), 99-115.
  • H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  • 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.
  • 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.
  • M. Turaev, Decomposition formulas for Srivastava's hypergeometric function $H_A$ on Saran functions, J. Comput. Appl. Math., 233 (2009), 842-846.