A NEW PROOF OF SAALSCHÜTZ`S THEOREM FOR THE SERIES _{3}F_{2}(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 27, Issue 1, 2012, pp.129-135
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2012.27.1.129

Title & Authors

A NEW PROOF OF SAALSCHÜTZ`S THEOREM FOR THE SERIES _{3}F_{2}(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS

Kim, Yong-Sup; Rathie, Arjun Kumar;

Kim, Yong-Sup; Rathie, Arjun Kumar;

Abstract

The aim of this paper is to establish the well-known and very useful classical Saalschtz`s theorem for the series (1) by following a different method. In addition to this, two summation formulas closely related to the Saalschtz`s theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series (1) and already available in the literature.

Keywords

Saalschtz`s theorem;integral transformation;Kummer`s transformation;Vandemonde`s theorem;

Language

English

References

1.

K. Arora and A. K. Rathie, Some summation formulas for the series $_3F_2$ ,Math. Ed. (Siwan) 28 (1994), no. 2, 111-112.

2.

A. Erdelyi et al., Tables of Integral Transforms. Vol. 2, McGraw Hill, New York, 1954.

3.

Y. S. Kim, T. K. Pogany, and A. K. Rathie, On a summation formula for the Clausen's series $_3F_2$ with applications, Miskolc Math. Notes 10 (2009), no. 2, 145-153.

4.

E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

5.

L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.