[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2007.44.4.743

ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X₈ DUE TO EXTON

Kim, Yong-Sup (DEPARTMENT OF MATHEMATICS EDUCATION WONKWANG UNIVERSITY)
Rathie, Arjun K. (DEPARTMENT OF MATHEMATICS GOVT. SUJANGARH COLLEGE)

Publication Information

Bulletin of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 743-751 More about this Journal

Abstract

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

Keywords

triple hypergeometric series $X_8$ ; laplace integral; $Kamp\acute{e}\; de\; F\acute{e}riet$ function; generalized Watson's theorem; the identities of Pochhammer symbol;

Citations & Related Records

Times Cited By Web Of Science : 2 (Related Records In Web of Science)
Times Cited By SCOPUS : 2

Reference
Cited By SCOPUS

1	Y. S. Kim, J. Choi, and A. K. Rathie, Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$ , submitted, Indian J. appl. Math
2	J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizatons of Watson's theorem on the sum of a $_3F_2$ , Indian J. Math. 34 (1992), no. 2, 23-32
3	W. N. Bailey, Generalized Hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York 1964
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	E. D. Rainville, Special functions, The Macmillan company, New York, 1960
7	H. M. Srivastava and H. L. Monacha, A Treatise on Generating Functions, Ellis Harwood limited, Chichester, 1984
8	H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
9	H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Harwood limited, Chichester, 1985

Reference
Cited By KSCI
Cited By SCOPUS

1	ON CERTAIN REDUCIBILITY OF KAMPE DE FERIET FUNCTION / [Kim, Yong-Sup;] / Honam Mathematical Journal
2	APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES ₂F₁ / [Kim, Yong-Sup;Rathie, Arjun K.;] / Bulletin of the Korean Mathematical Society
3	CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION $X_2$ / [Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali;] / The Pure and Applied Mathematics
4	GENERALIZED SINGLE INTEGRAL INVOLVING KAMPEÉ DE FÉRIET FUNCTION / [Kim, Yong Sup;Ali, Shoukat;Rathie, Navratna;] / Journal of the Chungcheong Mathematical Society
5	Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X₁₂ and X₁₇ / [Choi, Junesang;Rathie, Arjun K.;] / Kyungpook Mathematical Journal
6	CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X₅ / [Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali;] / Honam Mathematical Journal
7	AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON / [Lee, Seung-Woo;Kim, Yong-Sup;] / Honam Mathematical Journal
8	GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION / [Kim, Yong-Sup;Ali, Shoukat;Rathie, Navratna;] / Honam Mathematical Journal
9	DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS / [Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali;] / Journal of the Chungcheong Mathematical Society
10	CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X₈ / [Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali;] / Communications of the Korean Mathematical Society

6	Yong-Sup Kim. (2009) Bulletin of the Korean Mathematical Society APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES2F1 / 46 (6) , 1201
1	Yong-Sup Kim. (2011) Honam Mathematical Journal GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION / 33 (1) , 43
1	Seung-Woo Lee. (2010) Honam Mathematical Journal AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON / 32 (1) , 61
2	Yong-Sup Kim. (2009) Honam Mathematical Journal ON CERTAIN REDUCIBILITY OF KAMPE DE FERIET FUNCTION / 31 (2) , 167
4	Junesang Choi. (2014) Kyungpook mathematical journal Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17 / 54 (4) , 677
	Junesang Choi. (2010) Journal of Inequalities and Applications Contiguous Extensions of Dixon's Theorem on the Sum of a 3F2 / 2010 , 1
3	June-Sang Choi. (2010) Honam Mathematical Journal CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5 / 32 (3) , 389
1	Junesang Choi. (2013) Advances in Difference Equations Relations between Lauricella’s triple hypergeometric function FA(3)(x,y,z) and Exton’s function X8 / 2013 (1) , 34
2	June-Sang Choi. (2012) Communications of the Korean Mathematical Society CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8 / 27 (2) , 257

1	/ Bulletin of the Korean Mathematical Society
2	/ Journal of Inequalities and Applications

KSCI

ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X8 DUE TO EXTON

ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X₈ DUE TO EXTON