Global Analysis In Linear Differential Equations

Author: M. Kohno
Editor: Springer Science & Business Media
ISBN: 9401146055
File Size: 29,16 MB
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Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.
Global Analysis in Linear Differential Equations
Language: en
Pages: 528
Authors: M. Kohno
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The
Galois Theory of Linear Differential Equations
Language: en
Pages: 438
Authors: Marius van der Put, Michael F. Singer
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume
Divergent Series, Summability and Resurgence III
Language: en
Pages: 230
Authors: Eric Delabaere
Categories: Mathematics
Type: BOOK - Published: 2016-06-28 - Publisher: Springer

The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The
Complex Delay-Differential Equations
Language: en
Pages: 302
Authors: Kai Liu, Ilpo Laine, Lianzhong Yang
Categories: Mathematics
Type: BOOK - Published: 2021-05-25 - Publisher: Walter de Gruyter GmbH & Co KG

This book presents developments and new results on complex differential-difference equations, an area with important and interesting applications, which also gathers increasing attention. Key problems, methods, and results related to complex differential-difference equations are collected to offer an up-to-date overview of the field.
Asymptotic Integration of Differential and Difference Equations
Language: en
Pages: 402
Authors: Sigrun Bodine, Donald A. Lutz
Categories: Mathematics
Type: BOOK - Published: 2015-05-26 - Publisher: Springer

This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to