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CERTAIN SUMMATION FORMULAS DUE TO RAMANUJAN AND THEIR GENERALIZATIONS
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 Title & Authors
CERTAIN SUMMATION FORMULAS DUE TO RAMANUJAN AND THEIR GENERALIZATIONS
RATHIE ARJUN K.; MALANI SHALOO; MATHUR RACHANA; CHOI JUNESANG;
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 Abstract
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. The results are derived with the help of generalized Dixon's theorem obtained earlier by Lavoie, Grondin, Rathie, and Arora.
 Keywords
generalized hypergeometric series;Dixon's summation theorem;
 Language
English
 Cited by
1.
ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION,;;;

호남수학학술지, 2013. vol.35. 1, pp.83-92 crossref(new window)
1.
Generalizations of classical summation theorems for the series2F1and3F2with applications, Integral Transforms and Special Functions, 2011, 22, 11, 823  crossref(new windwow)
2.
GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN, Honam Mathematical Journal, 2012, 34, 1, 35  crossref(new windwow)
3.
ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION, Honam Mathematical Journal, 2013, 35, 1, 83  crossref(new windwow)
 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, 1987

3.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalization of Whipple's theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72 (1996), 293-300 crossref(new window)

4.
J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalization of Dixon's theorem on the sum of a $_3F_2$, Math. Comp. 62 (1994), 267-276 crossref(new window)

5.
H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001