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ISSN : 1226-0657

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Vol.20 No.1
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APPELL'S FUNCTION F<sub>1</sub> AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X<sub>9</sub>

APPELL'S FUNCTION F1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X9

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.1, pp.37-50
https://doi.org/10.7468/jksmeb.2013.20.1.37
Choi, Junesang (Department of Mathematics, Dongguk University)
Rathie, Arjun K. (Department of Mathematics, School of Mathematical & Physical Sciences, Central University of Kerala, Riverside Transit Campus)
Choi, Junesang, & Rathie, Arjun K.. (2013). APPELL'S FUNCTION F<sub>1</sub> AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X<sub>9</sub>. 한국수학교육학회지시리즈B:순수및응용수학, 20(1), 37-50, https://doi.org/10.7468/jksmeb.2013.20.1.37
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Abstract

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting explicit expressions (in a single form) of the following weighted Appell's function <TEX>$F_1$</TEX>: <TEX>$$(1+2x)^{-a}(1+2z)^{-b}F_1\;\(c,\;a,\;b;\;2c+j;\;\frac{4x}{1+2x},\;\frac{4z}{1+2z}\)\;(j=0,\;{\pm}1,\;{\ldots},\;{\pm}5)$$</TEX> in terms of Exton's triple hypergeometric <TEX>$X_9$</TEX>. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.

keywords
hypergeometric functions of several variables, multiple Gaussian hypergeometric series, Appell's function <tex> $F_1$</tex>, Exton's triple hypergeometric function <tex> $X_9$</tex>, Gauss's hypergeometric functions, generalizations of Kummer's second theorem

참고문헌

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한국수학교육학회지시리즈B:순수및응용수학

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