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The Hypergeometric Approach to Integral Transforms and Convolutions (Hardcover, 1994 ed.)
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The Hypergeometric Approach to Integral Transforms and Convolutions (Hardcover, 1994 ed.)
Series: Mathematics and Its Applications, 287
Expected to ship within 12 - 17 working days
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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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