CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8
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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 (X2, $X_8$) itself, the Horn's function H₄, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.
Abstract
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 (X2, $X_8$) itself, the Horn's function H₄, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.
참고문헌 (10)
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