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Global Analysis in Linear Differential Equations : Mathematics and Its Applications - Mitsuhiko Kohno

Global Analysis in Linear Differential Equations

Mathematics and Its Applications

Hardcover Published: 30th April 1999
ISBN: 9780792356059
Number Of Pages: 528

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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.

Gauss and Airy Equations
Linear Differential Equations
Reduction Problems
Monodromy Groups for Hypergeometric Systems
Connection Problem for Hypergeometric Systems
Stokes Phenomenon
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792356059
ISBN-10: 0792356055
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 528
Published: 30th April 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.4 x 17.0  x 3.81
Weight (kg): 2.08