대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권2호
  • /
  • Pages.257-264
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8

  • 투고 : 2010.09.29
  • 발행 : 2012.04.30
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초록

Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.

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참고문헌

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