CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8

Title & Authors
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8
Choi, June-Sang; Hasanov, Anvar; Turaev, Mamasali;

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