ON A NEW CLASS OF SERIES IDENTITIES

- Journal title : Honam Mathematical Journal
- Volume 37, Issue 3, 2015, pp.339-352
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2015.37.3.339

Title & Authors

ON A NEW CLASS OF SERIES IDENTITIES

SHEKHAWAT, NIDHI; CHOI, JUNESANG; RATHIE, ARJUN K.; PRAKASH, OM;

SHEKHAWAT, NIDHI; CHOI, JUNESANG; RATHIE, ARJUN K.; PRAKASH, OM;

Abstract

We aim at giving explicit expressions of , where i = 0, , , and is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

Keywords

Gamma function;Pochhammer symbol;Hypergeometric function;Generalized hypergeometric function;Generalized Kummer's summation theorem;

Language

English

References

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3.

J. Choi, Contiguous extensions of Dixon's theorem on the sum of a $_3F_2$ , J. Inequal. Appl. 2010 (2010), Article ID 589618.

4.

Y. S. Kim and A. K. Rathie, Application of generalized Kummer's summation theorem for the series $_2F_1$ , Bull. Koreon Math. Soc. 46(6) (2009), 1201-1211.

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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(2) (1996), 293-300.

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