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

Kim, Yong-Sup;Rathie, Arjun Kumar

  • Received : 2010.08.10
  • Published : 2012.01.31

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

  1. K. Arora and A. K. Rathie, Some summation formulas for the series $_3F_2$,Math. Ed. (Siwan) 28 (1994), no. 2, 111-112.
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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.
  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. https://doi.org/10.1112/plms/s2-25.1.525

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