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Global Analysis in Linear Differential Equations: 471 (Mathematics and Its Applications) - Hardcover
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.
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Reseña del editor
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.
Reseña del editor
This book 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.
Audience: This volume will be of interest to researchers and graduate students whose work involves ordinary differential equations, special functions, finite difference, functional equations, approximations and expansions, and symbolic/algebraic manipulation.
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Global Analysis in Linear Differential Equations
Verlag:
Springer Netherlands, Springer Netherlands Apr 1999, 1999
ISBN 10: 0792356055
ISBN 13: 9780792356059
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Buch. Zustand: Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 548 pp. Englisch. Artikel-Nr. 9780792356059
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Global Analysis in Linear Differential Equations
Verlag:
Springer Netherlands, Springer Netherlands, 1999
ISBN 10: 0792356055
ISBN 13: 9780792356059
Neu
Hardcover
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9780792356059
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Global Analysis in Linear Differential Equations (Mathematics and Its Applications, 471)
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