# 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)
• Accepted : 2013.02.12
• Published : 2013.03.25
• 90 24

#### 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

#### Acknowledgement

Supported by : Wonkwang University

#### References

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. https://doi.org/10.1016/0377-0427(95)00279-0
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. https://doi.org/10.4134/BKMS.2005.42.3.469
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.