Global Analysis in Linear Differential Equations (Hardcover)

M. Kohno

ISBN 10: 0792356055 / ISBN 13: 9780792356059

Verlag: Kluwer Academic Publishers, Dordrecht, 1999

Beschreibung

Hardcover. This work treats several topics on the global analysis of linear differential equations in the complex domain, using original methods of analysis developed by K. Okubo and the present author. For example, global analysis of linear differential equations is closely related to that of linear difference equations. Through the asymptotic behaviour of solutions of linear difference equations, connection problems for hypergeometric systems can be solved, i.e. Fuchsian differential equations and Stokes phenomenon for Birkhoff systems. Furthermore, the calculation of monodromy groups is explained in detail. 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. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Bestandsnummer des Verkäufers 9780792356059

Bibliografische Details

• Titel: Global Analysis in Linear Differential Equations (Hardcover)
• Verlag: Kluwer Academic Publishers, Dordrecht
• Erscheinungsjahr: 1999
• Sprache: Englisch
• ISBN-10: 0792356055
• ISBN-13: 9780792356059
• Einband: Hardcover
• Zustand: new

Über diesen Titel

Inhaltsangabe

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.