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A NEW PROOF OF SAALSCHÜTZ`S THEOREM FOR THE SERIES 3F2(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS
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 Title & Authors
A NEW PROOF OF SAALSCHÜTZ`S THEOREM FOR THE SERIES 3F2(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS
Kim, Yong-Sup; Rathie, Arjun Kumar;
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 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
 Cited by
 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.

6.
F. J. W. Whipple, Well-poised series and other generalized hypergeometric series, Proc. London Math. Soc. 25 (1926), no. 2, 525-544. crossref(new window)