Some integral representations of multivariable hypergeometric functions
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.
hypergeometric functions in several variables
scientific article; zbMATH DE number 91667
scientific article