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About this book
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.
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Table of contents (21 chapters)
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Front Matter
Authors and Affiliations
Bibliographic Information
Book Title: The Hypergeometric Approach to Integral Transforms and Convolutions
Authors: Semen B. Yakubovich, Yurii F. Luchko
Series Title: Mathematics and Its Applications
DOI: https://doi.org/10.1007/978-94-011-1196-6
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media Dordrecht 1994
Hardcover ISBN: 978-0-7923-2856-8Published: 31 May 1994
Softcover ISBN: 978-94-010-4523-0Published: 08 October 2012
eBook ISBN: 978-94-011-1196-6Published: 06 December 2012
Edition Number: 1
Number of Pages: XI, 324
Topics: Integral Transforms, Operational Calculus, Special Functions, Integral Equations