# A NEW PROOF OF SAALSCHÜTZ'S THEOREM FOR THE SERIES 3F2(1) AND ITS CONTIGUOUS RESULTS WITH APPLICATIONS

Kim, Yong-Sup;Rathie, Arjun Kumar

• Published : 2012.01.31
• 28 4

#### Abstract

The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz'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 $_3F_2$(1) and $_4F_3(1)$ already available in the literature.

#### Keywords

Saalsch$\ddot{u}$tz's theorem;integral transformation;Kummer's transformation;Vandemonde's theorem

#### References

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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.
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#### Cited by

1. Extensions of the classical theorems for very well-poised hypergeometric functions pp.1579-1505, 2017, https://doi.org/10.1007/s13398-017-0485-5