Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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EXTENSIONS OF EULER TYPE II TRANSFORMATION AND SAALSCHÜTZ'S THEOREM

  • Rakha, Medhat A. (DEPARTMENT OF MATHEMATICS AND STATISTICS COLLEGE OF SCIENCE SULTAN QABOOS UNIVERSITY, MATHEMATICS DEPARTMENT COLLEGE OF SCIENCE SUEZ CANAL UNIVERSITY) ;
  • Rathie, Arjun K. (VEDANT COLLEGE OF ENGINEERING AND TECHNOLOGY)
  • Received : 2009.05.29
  • Published : 2011.01.31
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Abstract

In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch$\ddot{u}$tz's summation theorem for the series $_3F_2$ has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch$\ddot{u}$tz's summation theorem are given.

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References

  1. W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc.(2) 28 (1928), 242-254. https://doi.org/10.1112/plms/s2-28.1.242
  2. A. P. Prudnikov, Iu. A. Brychkov, and O. I. Marichev, More Special Functions, Integralsand Series, Vol. 3, Gordon and Breach, New York, 1990.
  3. A. K. Rathie and R. B. Paris, An extension of the Euler-type transformation for the $_3F_2$series, Far East J. Math. Sci. (FJMS) 27 (2007), no. 1, 43-48.

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  2. A NEW PROOF OF THE EXTENDED SAALSCHÜTZ'S SUMMATION THEOREM FOR THE SERIES4F3AND ITS APPLICATIONS vol.35, pp.3, 2013, https://doi.org/10.5831/HMJ.2013.35.3.407
  3. Extension of a quadratic transformation due to Whipple with an application vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-157