Some integral representations of multivariable hypergeometric functions
Copyright policy )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.
- Fukuoka University Japan
- Institute of Mathematics Viet Nam
- Fukuoka University Japan
hypergeometric functions in several variables, Gauss function, Integral transforms of special functions, multiple integral representations, Kampé de Fériet function, Lauricella functions, Other hypergeometric functions and integrals in several variables, Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Kummer function, modified Bessel functions, Special integral transforms (Legendre, Hilbert, etc.), Mellin transformation
hypergeometric functions in several variables, Gauss function, Integral transforms of special functions, multiple integral representations, Kampé de Fériet function, Lauricella functions, Other hypergeometric functions and integrals in several variables, Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Kummer function, modified Bessel functions, Special integral transforms (Legendre, Hilbert, etc.), Mellin transformation
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