The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION $X_2$

  • Received : 2010.07.27
  • Accepted : 2010.11.20
  • Published : 2010.11.30
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Abstract

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_oF_1$, $_1F_1$, a Humbert function ${\Psi}_2$, a Humbert function ${\Phi}_2$. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function $X_2$ among his twenty $X_i$ (i = 1, ..., 20), whose kernels include the Exton function $X_2$ itself, the Appell function $F_4$, and the Lauricella function $F_C$.

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References

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