Kyungpook Mathematical Journal

  • 제47권3호
  • /
  • Pages.449-454
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  • 2007
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Generalizations of Dixon's and Whipple's Theorems on the Sum of a 3F2

  • 투고 : 2006.03.21
  • 발행 : 2007.09.23
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초록

InIn this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a $_3F_2$. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings.

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참고문헌

  1. W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, (1935).
  2. J. Choi, A. K. Rathie and S. Malani, A Summation Formula of $_{6}F_{5}$(1), Comm. Korean Math. Soc., 19(2004), 775-778. https://doi.org/10.4134/CKMS.2004.19.4.775
  3. J. L. Lavoie, F. Grondin and A. K. Rathie, Generalizations of Watson's theorem on the sum of a $_{3}F_{2}$, Indian J. Math., 34(1992), 23-32.
  4. J. L. Lavoie, F. Grondin and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$, J. Comput. Appl. Math., 72(1996), 293-300. https://doi.org/10.1016/0377-0427(95)00279-0
  5. J. L. Lavoie, F. Grondin, A. K. Rathie and K. Arora, Generalizations of Dixon's theorem on the sum of a $_{3}F_{2}$, Math. Comput., 49(1987), 269-274.
  6. S. C. Mitra, J. Indian Math. Soc., 7(3)(1943), 102-110.