Format:
1 Online-Ressource (viii, 243 pages)
,
digital, PDF file(s).
ISBN:
9780511753626
Series Statement:
Encyclopedia of mathematics and its applications volume 141
Content:
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics.
Content:
Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9781107002586
Additional Edition:
ISBN 9781107002586
Additional Edition:
Erscheint auch als Paris, Richard B. Hadamard expansions and hyperasymptotic evaluation Cambridge [u.a.] : Cambridge University Press, 2011 ISBN 9781107002586
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781107002586
Language:
English
Keywords:
Integralgleichung
;
Asymptotik
;
Laplace-Transformation
DOI:
10.1017/CBO9780511753626
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