[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2006.21.3.569

GENERALIZATIONS OF GAUSS'S SECOND SUMMATION THEOREM AND BAILEY'S FORMULA FOR THE SERIES ₂F₁(1/2)

Rathie, Arjun K. (Department of Mathematics Govt. Sujangarh College Distt.)
Kim, Yong-Sup (Department of Mathematics WonKwang University)
Choi, June-Sang (Department of Mathematics College of Natural Sciences, Dongguk University)

Publication Information

Communications of the Korean Mathematical Society / v.21, no.3, 2006 , pp. 569-575 More about this Journal

Abstract

We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series $_2F_1(1/2)$ . An interesting transformation formula for $_pF_q$ is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.

Keywords

generalized hypergeometric series $_pF_q$ ; summation theorems for $_pF_q$ ;

Citations & Related Records

Reference

1	W. N. Bailey, An extension of Whipple's theorem on well poised hypergeometric series, Proc. London Math. Soc. (2) 31 (1929), 505-512
2	F. J. W. Whipple, Some transformations of generalized hypergeometric series, Proc. London Math. Soc. (2) 26 (1927), 257-272
3	W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935
4	J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_2$ , J. Comput. Appl. Math. 72 (1996), 293-300 DOI ScienceOn
5	H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001

KSCI

GENERALIZATIONS OF GAUSS'S SECOND SUMMATION THEOREM AND BAILEY'S FORMULA FOR THE SERIES 2F1(1/2)

GENERALIZATIONS OF GAUSS'S SECOND SUMMATION THEOREM AND BAILEY'S FORMULA FOR THE SERIES ₂F₁(1/2)