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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.20 No.1

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

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
2013, v.20 no.1, pp.37-50
https://doi.org/10.7468/jksmeb.2013.20.1.37
Choi, Junesang
Rathie, Arjun K.
Choi,, J. , & Rathie,, A. K. (2013). APPELL'S FUNCTION F1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X9. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(1), 37-50, https://doi.org/10.7468/jksmeb.2013.20.1.37

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

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

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