The Hypergeometric Approach to Integral Transforms and Convolutions (Paperback, Softcover reprint of the original 1st ed. 1994)

The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special functions, and convolutions. The idea of this approach can be found in various papers of many authors, but systematic discussion and development is realized in this book for the first time. Let us explain briefly the basic points of this approach. As it is known, in the theory of special functions and its applications, the hypergeometric functions play the main role. Besides known elementary functions, this class includes the Gauss's, Bessel's, Kummer's, functions et c. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These ques tions are extensively discussed in Chapter 1. Moreover, the Mellin-Barnes type integrals can be understood as an inversion Mellin transform from the quotient of products of Euler's gamma-functions. Thus we are led to the general construc tions like the Meijer's G-function and the Fox's H-function."

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 287
Release date:	October 2012
First published:	1994
Authors:	S. B. Yakubovich • Yury Luchko
Dimensions:	235 x 155 x 18mm (L x W x T)
Format:	Paperback
Pages:	324
Edition:	Softcover reprint of the original 1st ed. 1994
ISBN-13:	978-9401045230
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	9401045232
Barcode:	9789401045230

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