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The Hypergeometric Approach to Integral Transforms and Convolutions

  • Semen B. Yakubovich
  • Yurii F. Luchko

Part of the Mathematics and Its Applications book series (MAIA, volume 287)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Semen B. Yakubovich, Yurii F. Luchko
    Pages 1-14
  3. Semen B. Yakubovich, Yurii F. Luchko
    Pages 15-40
  4. Semen B. Yakubovich, Yurii F. Luchko
    Pages 41-58
  5. Semen B. Yakubovich, Yurii F. Luchko
    Pages 59-68
  6. Semen B. Yakubovich, Yurii F. Luchko
    Pages 69-78
  7. Semen B. Yakubovich, Yurii F. Luchko
    Pages 79-108
  8. Semen B. Yakubovich, Yurii F. Luchko
    Pages 109-138
  9. Semen B. Yakubovich, Yurii F. Luchko
    Pages 139-148
  10. Semen B. Yakubovich, Yurii F. Luchko
    Pages 149-166
  11. Semen B. Yakubovich, Yurii F. Luchko
    Pages 167-172
  12. Semen B. Yakubovich, Yurii F. Luchko
    Pages 173-182
  13. Semen B. Yakubovich, Yurii F. Luchko
    Pages 183-188
  14. Semen B. Yakubovich, Yurii F. Luchko
    Pages 189-204
  15. Semen B. Yakubovich, Yurii F. Luchko
    Pages 205-212
  16. Semen B. Yakubovich, Yurii F. Luchko
    Pages 213-228
  17. Semen B. Yakubovich, Yurii F. Luchko
    Pages 229-240
  18. Semen B. Yakubovich, Yurii F. Luchko
    Pages 241-252
  19. Semen B. Yakubovich, Yurii F. Luchko
    Pages 253-264
  20. Semen B. Yakubovich, Yurii F. Luchko
    Pages 265-276
  21. Semen B. Yakubovich, Yurii F. Luchko
    Pages 277-286
  22. Semen B. Yakubovich, Yurii F. Luchko
    Pages 287-294
  23. Back Matter
    Pages 295-324

About this book

Introduction

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.

Keywords

Cauchy problem Integral equation convolution differential equation differential operator integral transform operational calculus

Authors and affiliations

  • Semen B. Yakubovich
    • 1
  • Yurii F. Luchko
    • 1
  1. 1.Department of Mathematics and MechanicsBeylorussian State UniversityMinsk, ByelorussiaRussia

Bibliographic information

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