GENERALIZATIONS OF GAUSS'S SECOND SUMMATION THEOREM AND BAILEY'S FORMULA FOR THE SERIES _{2}F_{1}(1/2)

- Journal title : Communications of the Korean Mathematical Society
- Volume 21, Issue 3, 2006, pp.569-575
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2006.21.3.569

Title & Authors

GENERALIZATIONS OF GAUSS'S SECOND SUMMATION THEOREM AND BAILEY'S FORMULA FOR THE SERIES _{2}F_{1}(1/2)

Rathie, Arjun K.; Kim, Yong-Sup; Choi, June-Sang;

Rathie, Arjun K.; Kim, Yong-Sup; Choi, June-Sang;

Abstract

We aim mainly at presenting two generalizations of the well-known Gauss's second summation theorem and Bailey's formula for the series . An interesting transformation formula for is obtained by combining our two main results. Relevant connections of some special cases of our main results with those given here or elsewhere are also pointed out.

Keywords

generalized hypergeometric series ;summation theorems for ;

Language

English

References

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W. N. Bailey, An extension of Whipple's theorem on well poised hypergeometric series, Proc. London Math. Soc. (2) 31 (1929), 505-512

2.

W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935

3.

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 (1996), 293-300

4.

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

5.

F. J. W. Whipple, Some transformations of generalized hypergeometric series, Proc. London Math. Soc. (2) 26 (1927), 257-272