[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5831/HMJ.2013.35.1.83

ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION

Lee, Seung Woo (Department of Mathematics, Wonkwang University)
Lee, Chang Hyun (Department of Mathematics, Seonam University)
Kim, Yong Sup (Department of Mathematics Education, Wonkwang University)

Publication Information

Honam Mathematical Journal / v.35, no.1, 2013 , pp. 83-92 More about this Journal

Abstract

The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of $_3F_2$ and the generalized Kummer's theorem for $_2F_1$ obtained earlier by Lavoie et al. [3, 5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

Keywords

Hypergeometric $_2F_1$ ; Dixon's summation theorem; Kummer's summation theorem; Ramanujan summation formula;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	W.N Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.
2	B.C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, New York, 1985.
3	J.L. Lavoie, F. Grondin, A.K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a $_3F_2$ , Math. Comp. 62(205) (1994), 267-276.
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(2) (1996), 293-300. DOI ScienceOn
5	T.K. Pogany, A.K. Rathie, and U. Pandey, Generalization of a summation due to Ramanujan, Makedon. Akad. Nauk. Umet. Oddel. Mat.-Tehn. Nauk. Prilozi XXX(1-2) (2009), 67-73.
6	A.K. Rathie, S. Malani, R. Mathur, and J. Choi, Certain summations due to Ramanujan and their generalizations, Bull. Korean Math. Soc. 42(3) (2005), 469-475. DOI ScienceOn
7	M.R. Spiegel, Mathematical Handbook, Mc Graw-Hill Book Company, New York, 1968.
8	H.M. Srivastava and J. Choi, Zeta and q-zeta functions and associated series and integrals, Elsevier Science Publishers, Amsterdam, London, and New York, 2012.