- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Certain integral representations of Euler type for the Exton function $X_8$ Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 257-264 https://doi.org/10.4134/CKMS.2012.27.2.257Printed June 1, 2012 Junesang Choi, Anvar Hasanov, and Mamasali Turaev Dongguk University, Dongguk University, Dongguk University 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 ($X_2$, $X_8$) 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 $X_8$. Keywords : generalized hypergeometric series, multiple hypergeometric functions, integrals of Euler type, Laplace integral, Exton functions $X_i$, Humbert functions, Appell-Horn function $H_4$, Lauricella hypergeometric function $F_C$ MSC numbers : Primary 33C20, 33C65; Secondary 33C05, 33C60, 33C70, 68Q40, 11Y35 Downloads: Full-text PDF

 Copyright © Korean Mathematical Society. (Rm.1109) The first building, 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd