H-Transforms
Subtitle: Theory and Applications (Analytical Methods and Special Functions, 9)
Publisher: CRC
Published: March 15, 2004
Language: eng
Number of pages: 389
ISBN-13: 9780415299169
First sentence: For integers m, n, q such that 0 m q, 0 n p, for ai, bj, C with C, the set of complex numbers, and for ai, Bj R+ = (0,) (i = 1, 2, ..., p; j = 1, 2, ..., q), the H-function Hp,q m,n (z) is defined via a Mellin-Barnes type integral in the form (1.1.1) with.
Description: "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.