CERTAIN SUMMATION FORMULAS DUE TO RAMANUJAN AND THEIR GENERALIZATIONS

• RATHIE ARJUN K. ;
• MALANI SHALOO ;
• MATHUR RACHANA ;
• CHOI JUNESANG
• Published : 2005.08.01
• 52 5

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

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 https://doi.org/10.1016/0377-0427(95)00279-0
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 https://doi.org/10.2307/2153407
5. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001

Cited by

1. Generalizations of classical summation theorems for the series2F1and3F2with applications vol.22, pp.11, 2011, https://doi.org/10.1080/10652469.2010.549487
2. GENERALIZATIONS OF CERTAIN SUMMATION FORMULA DUE TO RAMANUJAN vol.34, pp.1, 2012, https://doi.org/10.5831/HMJ.2012.34.1.35
3. ANOTHER GENERALIZATION OF A RAMANUJAN SUMMATION vol.35, pp.1, 2013, https://doi.org/10.5831/HMJ.2013.35.1.83