The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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FURTHER SUMMATION FORMULAS FOR THE APPELL'S FUNCTION $F_1$

  • CHOI JUNESANG (DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCES, DONGGUK UNIVERSITY) ;
  • HARSH HARSHVARDHAN (DEPT. OF MATHEMATICS, DUNGAR COLLEGE, BIKANER UNIVERSITY) ;
  • RATHIE ARJUN K. (DEPARTMENT OF MATHEMATICS, DUNGAR COLLEGE, BIKANER UNIVERSITY)
  • Published : 2005.08.01
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Abstract

In 2001, Choi, Harsh & Rathie [Some summation formulas for the Appell's function $F_1$. East Asian Math. J. 17 (2001), 233-237] have obtained 11 results for the Appell's function $F_1$ with the help of Gauss's summation theorem and generalized Kummer's summation theorem. We aim at presenting 22 more results for $F_1$ with the help of the generalized Gauss's second summation theorem and generalized Bailey's theorem obtained by Lavoie, Grondin & Rathie [Generalizations of Whipple's theorem on the sum of a $_3F_2$. J. Comput. Appl. Math. 72 (1996), 293-300]. Two interesting (presumably) new special cases of our results for $F_1$ are also explicitly pointed out.

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