Further Summation formulas for the Appell's Function $F_1$

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2005, v.12 no.3, pp.223-228

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)

CHOI JUNESANG, HARSH HARSHVARDHAN, & RATHIE ARJUN K.. (2005). FURTHER SUMMATION FORMULAS FOR THE APPELL'S FUNCTION <TEX>$F_1$</TEX>. 한국수학교육학회지시리즈B:순수및응용수학, 12(3), 223-228.

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Abstract

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

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Vol.12 No.3

FURTHER SUMMATION FORMULAS FOR THE APPELL'S FUNCTION <TEX>$F_1$</TEX>

Further Summation formulas for the Appell's Function $F_1$

Abstract

한국수학교육학회지시리즈B:순수및응용수학