The Hypergeometric Approach to Integral Transforms and Convolutions

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The Hypergeometric Approach to Integral Transforms and Convolutions is written by S. Semen B. Yakubovich and published by Kluwer Academic Pub. It's available with International Standard Book Number or ISBN identification 0792328566 (ISBN 10) and 9780792328568 (ISBN 13).

This volume deals with the theory and applications of integral transforms and convolutions of certain classes of integral, integrodifferential equations, and operational calculus. An extensive discussion is presented, based on the universal hypergeometric approach, i.e. many constructions of convolution and integral transforms are obtained using the theory of Mellin--Barnes integrals and the Mellin transforms of hypergeometric type functions. This approach is spread on so-called index transforms, in which the Kontorovich--Lebedev and the Mehler--Fock transforms play a very important part. The general constructions of index transforms are given and application to the evaluation of improper integral with respect to a parameter of special function (index) is considered. The operational calculus for general integrodifferential operators is constructed for both new types of convolutions. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography. This work will be of interest to researchers and graduate students in the mathematical and physical sciences whose work involves integral transforms and convolutions.