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

ISSN : 3059-0604

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Vol.19 No.2

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INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.2, pp.137-145
https://doi.org/10.7468/jksmeb.2012.19.2.137
Choi, June-Sang (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)
Choi, June-Sang, Hasanov, Anvar, & Turaev, Mamasali. (2012). INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION H<sub>B</sub>, 19(2), 137-145, https://doi.org/10.7468/jksmeb.2012.19.2.137

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 the Srivatava's triple hypergeometric function $H_B$.

keywords
multiple hypergeometric functions, Gauss hypergeometric function <tex> $_2F_1$</tex>, confluent hypergeometric functions, Eulerian integrals, Laplace integrals, Srivastava's triple hypergeometric function <tex> $H_B$</tex>, Exton's functions, Humbert functions, Bessel functions, beta and gamma functions, Appell functions, Picard's integral formula

참고문헌

1.

Fonctions Hypergeometriques et Hyperspheriques; Polynomes d'Hermite.

2.

(2011). Integral representations for Srivastava's triple hypergeometric functions. Taiwanese J. Math., 15, 2751-2762.

3.

Higher Transcendental Functions. Vol. I.

4.

(1982). Hypergeometric functions of three variables. J. Indian Acad. Math., 4, 113-119.

5.

(2006). Some decomposition formulas associated with the Lauricella function <TEX>$F_A^{(r)}$</TEX> and other multiple hypergeometric functions. Appl. Math. Lett., 19, 113-121. 10.1016/j.aml.2005.03.009.

6.

(2007). Decomposition formulas associated with the Lauricella multivariable hypergeometric functions. Comput. Math. Appl., 53, 1119-1128. 10.1016/j.camwa.2006.07.007.

7.

(2006). Decomposition formulas for some triple hypergeometric functions. J. Math. Anal. Appl., 324, 955-969. 10.1016/j.jmaa.2006.01.006.

8.

(1893). Sulle funzioni ipergeometriche a piu variabili. Rend. Circ. Mat. Palermo, 7, 111-158. 10.1007/BF03012437.

9.

(1999). Two results on three variable hypergeometric function. Indian J. Pure Appl. Math., 30, 1107-1109.

10.

(1954). Hypergeometric functions of three variables. Ganita, 5, 71-91.

11.

(1964). Hypergeometric functions of three variables. Ganita, 15, 97-108.

12.

(1967). Some integrals representing triple hypergeometric functions. Rend. Circ. Mat. Palermo, 16, 99-115. 10.1007/BF02844089.

13.

Series Associated with the Zeta and Related Functions.

14.

Zeta and q-Zeta Functions and Associated Series and Integrals.

15.

Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester).

16.

A Treatise on Generating Functions. Halsted Press (Ellis Horwood Limited, Chichester).

17.

(2009). Decomposition formulas for Srivastava's hypergeometric function <TEX>$H_A$</TEX> on Saran functions. J. Comput. Appl. Math., 233, 842-846. 10.1016/j.cam.2009.02.050.

한국수학교육학회지시리즈B:순수및응용수학

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