Browse > Article
http://dx.doi.org/10.5831/HMJ.2010.32.1.061

AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON  

Lee, Seung-Woo (Department of Mathematics, Wonkwang University)
Kim, Yong-Sup (Department of Mathematics Education, Wonkwang University)
Publication Information
Honam Mathematical Journal / v.32, no.1, 2010 , pp. 61-71 More about this Journal
Abstract
The aim of this paper is to extend a number of transformation formulas for the four $X_4$, $X_5$, $X_7$, and $X_8$ among twenty triple hypergeometric series $X_1$ to $X_{20}$ introduced earlier by Exton. The results are derived from the generalized Kummer's theorem and Dixon's theorem obtained earlier by Lavoie et al..
Keywords
Triple hypergeometric series; Generalized Kummer's theorem for $_2F_1(-1)$; Generalized Dixon's summation theorem for $_3F_2(1)$;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 J. L. Lavoie, F. grodin, A. K. Rathie and K. Arora Generalizations of Dixon's theorem on the sum of a $_3F_2$, Marhematics of Computation 62, No.205 (1994), 267-276.
2 E. D. Rainville, Special functions, Macmillan Company, New York, 1960.
3 H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001.
4 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.
5 H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1984.
6 Y. S. Kim, J. Choi and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series Xs, Honam Math. Journal 27 (4) (2005), 603-608.
7 W. N. Bailey, Generalized hypergeometric series, Cambridge Tracts in math., 1935 Reprinted by Stechert-Hefner, New York, 1964.
8 J. Choi, Notes on formal manipulations of double series, Commun. of Korean Math. Soc. 18 (4) (2003), 781-789.   과학기술학회마을   DOI   ScienceOn
9 H. Exton, Hypergeometric function of three variables, J. Indian Aced. Maths. 4(2) (1982), 113-119.
10 Y. S. Kim and A. K. Rathie, On an extension formulas for the triple hypergeometric series Xs due to Exton, Bull. Korean Math. Soc. 44 (4) (2007), 743-751.   DOI   ScienceOn
11 Y. S. Kim and A. K. Rathie, Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series Xs, Commu. of Korean Math. Soc. 24 (4) (2009), 517- 521.   DOI   ScienceOn
12 J. L. Lavoie, F. grodin and A. K. Rathie, Generalizations of Watson's theorem on the sum of a $_3F_2$, Indian J. Math. 34 (2) (1992), 23-32.
13 J. L. Lavoie, F. grodin and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_2$, Journal of Computational and Applied Mathematics 72 (1996), 293-300.   DOI   ScienceOn