호남수학학술지 (Honam Mathematical Journal)

  • 제26권1호
  • /
  • Pages.119-132
  • /
  • 2004
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

GENERALIZATION OF WHIPPLE'S THEOREM FOR DOUBLE SERIES

  • RATHIE, ARJUN K. (Department of Mathematics, Govt. Dungar College(M.D.S. University)) ;
  • GAUR, VIMAL K. (Department of Mathematics, Govt. Girls College) ;
  • KIM, YONG SUP (Department of Mathematics, Institute of Basic Natural Science, Wonkwang University) ;
  • PARK, CHAN BONG (Department of Mathematics, Wonkwang University)
  • 투고 : 2003.10.29
  • 심사 : 2003.11.17
  • 발행 : 2004.03.25
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초록

In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.

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과제정보

연구 과제 주관 기관 : Wonkwang University

참고문헌

  1. Gerneralized Hypergeometric series, Cambridge Math. Tract. No. 32;Stechert-Hafner Bailey, W.N.
  2. Ganita v.16 On certain sums and transformations of hypergeometric functions of two variables of superior order Bhatt, R.C.;Pandey, R.C.
  3. C.R. Acad. Sci. Paris v.173 Les fonctions hypergeometriques dordre superieur a deux variables Kampe de Feriet, J.
  4. Indian J. Math. v.34 Generalizations of Watson's theorem on the sum of $a_3F_2$ Lavoie, J.L.;Grondin, F.;Rathie, A.K.
  5. J. London Math. Soc. v.12 no.2 An integral representation for the product of two Jacobi Polynomials Srivastava, H.M.;Panda, R.