JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 34, Issue 1,  2012, pp.35-44
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2012.34.1.35
 Title & Authors
GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN
Song, Hyeong-Kee; Kim, Yong-Sup;
  PDF(new window)
 Abstract
Motivated by the extension of classical Dixon's summation theorem for the series given by Lavoie, Grondin, Rathie and Arora, the authors aim at deriving four generalized summation formulas, which, upon specializing their parameters, give many summation identities including, especially, the four very interesting summation formulas due to Ramanujan.
 Keywords
generalized hypergeometric series;generalized Dixon's summation theorem;Ramanujan summation formula;
 Language
English
 Cited by
 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.
Y.S. Kim and A.K. Rathie, Applications of generalized Kummer's summation theorem for the series $_{2}F_{2}$, Bull. Korean Math. Soc. 46 (2009), No. 6, 1201-1211. crossref(new window)

4.
Y.S. Kim, M.A. Rakha and A.K. Rathie, Extensions of certain classical summa- tion theorem for the series $_{2}F_{2}$, $_{3}F_{2}$ and $_{4}F_{3}$ with applications in Ramanujan's summations, Internat. J. Math. Math. Sci. 2010, pp.1-26, Article ID 309503.

5.
J.L. Lavoie, F. Grondin, A.K. Rathie and K. Arora, Generalizations of Dixon's theorem on the sum of a $_{3}F_{2}$,Math. Comp. 62(205) (1994), 267-276.

6.
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.

7.
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. crossref(new window)

8.
L.J. Slater, Generalized hypergeometric functions, Ccmbridge, 1966.

9.
H.M. Srivastava and J. Choi, Series Associated with the Zeta and related functions, Kluwer Academic Publishers, Dordrecht, 2001. MR2003a:11107