H-transforms

the long version

"H-Transforms : Theory and Applications presents a unified approach to the study of a wide class of integral transforms involving special functions as kernels. This approach is based on studying more general integral transforms with H-function kernels. The authors establish the properties, the representation, and the range of such H-transforms and prove their inversion relations." "The authors base their investigation on the method of Mellin multipliers and on the asymptotic analysis of the H-function at zero and infinity. This allows them not only to characterize the theory of H-transforms, but also to extend the h-function to a more general range of parameters, construct the theory of this function, and define more precisely its known properties." "This treatment includes applications to integral transforms with kernels containing Meijer's G-function and various special functions, such as hypergeometric type functions, transforms containing Whittaker and parabolic cylinder functions, and Bessel-type functions. It includes a thorough survey of results in the theory of H- and G-transforms and of integral transforms with hypergeometric and Bessel function kernels and a full bibliography."--BOOK JACKET.