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

CHOI JUNESANG; CHOI JUNESANG; HARSH HARSHVARDHAN; HARSH HARSHVARDHAN; RATHIE ARJUN K.; RATHIE ARJUN K.

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.12 No.3

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
HARSH HARSHVARDHAN
RATHIE ARJUN K.

CHOI, J. , HARSH, H. , & RATHIE, A. K. (2005). Further Summation formulas for the Appell's Function $F_1$. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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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Article Contents

Vol.12 No.3

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

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics