Browse > Article
http://dx.doi.org/10.4134/CKMS.2014.29.1.097

DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY  

Hayashi, Naoya (Josho Gakuen High School)
Matsui, Yutaka (Department of Mathematics Kinki University)
Publication Information
Communications of the Korean Mathematical Society / v.29, no.1, 2014 , pp. 97-108 More about this Journal
Abstract
In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeometric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions.
Keywords
generalized hypergeometric functions; Gauss-Kummer identity; decomposition formulae;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric functions, Quart. J. Math. Oxford Ser. 11 (1940), 249-270.
2 J. L. Burchnall and T. W. Chaundy, Expansions of Appell's double hypergeometric function. II, Quart. J. Math. Oxford Ser. 12 (1941), 112-128.
3 T. W. Chaundy, Expansions of hypergeometric functions, Quart. J. Math. Oxford Ser. 13 (1942), 159-171.
4 J. Choi and A. Hasanov, Applications of the operator H(${\alpha}$, ${\beta}$) to the Humbert double hypergeometric functions, Comput. Math. Appl. 61 (2011), no. 3, 663-671.   DOI   ScienceOn
5 J. Choi and A. Hasanov, Certain decomposition formulas of generalized hypergeometric functions $_pF_q$ and some formulas of an analytic continuation of the Clausen function $_3F_2$, Commun. Korean Math. Soc. 27 (2012), no. 1, 107-116.   과학기술학회마을   DOI   ScienceOn
6 A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F_A^{({\gamma})}$ and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), no. 2, 113-121.   DOI   ScienceOn
7 A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Compt. Math. Appl. 53 (2007), no. 7, 1119-1128.   DOI   ScienceOn
8 A. Hasanov, H. M. Srivastava, and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), no. 2, 955-969.   DOI   ScienceOn
9 A. Hasanov, M. Turaev, and J. Choi, Decomposition formulas for the generalized hypergeometric $_4F_3$ function, Honam Math. J. 32 (2010), no. 1, 1-16.   DOI   ScienceOn
10 K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida, From Gauss to Painleve, A modern theory of special functions, Aspects of Mathematics, E16, Friedr. Vieveg & Sohn, Braunschweig, 1991.
11 H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted press, Wiley, New York, 1985.