한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제20권1호
  • /
  • Pages.37-50
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  • 2013
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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APPELL'S FUNCTION F1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X9

  • 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)
  • 투고 : 2012.11.20
  • 심사 : 2013.01.14
  • 발행 : 2013.02.28
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초록

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 $F_1$: $$(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)$$ in terms of Exton's triple hypergeometric $X_9$. 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.

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참고문헌

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