The Hypergeometric Approach to Integral Transforms and Convolutions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1994
|
| Series: | Mathematics and Its Applications
287 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The aim of this book is to develop a new approach which we called the hypergeometric 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 etc. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These questions 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 constructions like the Meijer's G-function and the Fox's H-function |
| Physical Description: | 1 Online-Ressource (XI, 324 p) |
| ISBN: | 9789401111966 9789401045230 |
| DOI: | 10.1007/978-94-011-1196-6 |
Staff View
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| 500 | |a The aim of this book is to develop a new approach which we called the hypergeometric 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 etc. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These questions 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 constructions like the Meijer's G-function and the Fox's H-function | ||
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| institution | BVB |
| isbn | 9789401111966 9789401045230 |
| language | English |
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| spelling | Yakubovich, Semen B. Verfasser aut The Hypergeometric Approach to Integral Transforms and Convolutions by Semen B. Yakubovich, Yurii F. Luchko Dordrecht Springer Netherlands 1994 1 Online-Ressource (XI, 324 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 287 The aim of this book is to develop a new approach which we called the hypergeometric 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 etc. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These questions 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 constructions like the Meijer's G-function and the Fox's H-function Mathematics Integral equations Integral Transforms Functions, special Integral Transforms, Operational Calculus Special Functions Integral Equations Mathematik Integraltransformation (DE-588)4027235-7 gnd rswk-swf Hypergeometrische Reihe (DE-588)4161061-1 gnd rswk-swf Hypergeometrische Reihe (DE-588)4161061-1 s Integraltransformation (DE-588)4027235-7 s 1\p DE-604 Luchko, Yurii F. Sonstige oth Mathematics and Its Applications 287 (DE-604)BV008163334 287 https://doi.org/10.1007/978-94-011-1196-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yakubovich, Semen B. The Hypergeometric Approach to Integral Transforms and Convolutions Mathematics and Its Applications Mathematics Integral equations Integral Transforms Functions, special Integral Transforms, Operational Calculus Special Functions Integral Equations Mathematik Integraltransformation (DE-588)4027235-7 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| subject_GND | (DE-588)4027235-7 (DE-588)4161061-1 |
| title | The Hypergeometric Approach to Integral Transforms and Convolutions |
| title_auth | The Hypergeometric Approach to Integral Transforms and Convolutions |
| title_exact_search | The Hypergeometric Approach to Integral Transforms and Convolutions |
| title_full | The Hypergeometric Approach to Integral Transforms and Convolutions by Semen B. Yakubovich, Yurii F. Luchko |
| title_fullStr | The Hypergeometric Approach to Integral Transforms and Convolutions by Semen B. Yakubovich, Yurii F. Luchko |
| title_full_unstemmed | The Hypergeometric Approach to Integral Transforms and Convolutions by Semen B. Yakubovich, Yurii F. Luchko |
| title_short | The Hypergeometric Approach to Integral Transforms and Convolutions |
| title_sort | the hypergeometric approach to integral transforms and convolutions |
| topic | Mathematics Integral equations Integral Transforms Functions, special Integral Transforms, Operational Calculus Special Functions Integral Equations Mathematik Integraltransformation (DE-588)4027235-7 gnd Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| topic_facet | Mathematics Integral equations Integral Transforms Functions, special Integral Transforms, Operational Calculus Special Functions Integral Equations Mathematik Integraltransformation Hypergeometrische Reihe |
| url | https://doi.org/10.1007/978-94-011-1196-6 |
| volume_link | (DE-604)BV008163334 |
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