Some integral representations of multivariable hypergeometric functions
type: Item
instance of: scholarly article
title: Some integral representations of multivariable hypergeometric functions
zbMATH Open document ID: 0752.33006
DOI: 10.1007/BF02844464
author: Megumi Saigo
author: Vu Kim Tuan
publication date: 1993-01-16T00:00:00Z
review text: The \(n\)-dimensional Mellin transformation is applied in order to obtain two interesting multiple integral representations of the Kampé de Fériet function in \(n\)-variables. Corollaries of these results are \(n\)- dimensional integral representations for pairs of the Lauricella functions \(F_ D^{(n)}\), \(F_ B^{(n)}\), and \(F_ A^{(n)}\), \(F_ C^{(n)}\). These formulas provide generalizations of the representation of the Gauss function \(_ 2F_ 1\) as an integral involving first the Kummer function and second the modified Bessel functions.
Mathematics Subject Classification ID: 33C70
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 44A20
zbMATH DE Number: 91667
zbMATH Keywords: hypergeometric functions in several variables
zbMATH Keywords: Mellin transformation
zbMATH Keywords: multiple integral representations
zbMATH Keywords: Kampé de Fériet function
zbMATH Keywords: Lauricella functions
zbMATH Keywords: Gauss function
zbMATH Keywords: Kummer function
zbMATH Keywords: modified Bessel functions
reviewed by: Robert G. Buschman
MaRDI profile type: Publication
cites work: Q4157010
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 91667