대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제48권1호
  • /
  • Pages.151-156
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  • 2011
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2009.05.29
  • 발행 : 2011.01.31
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초록

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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참고문헌

  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, Integrals and 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.

피인용 문헌

  1. An extension of Saalschütz's summation theorem for the seriesr+3Fr+2 vol.24, pp.11, 2013, https://doi.org/10.1080/10652469.2013.777721
  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