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Hadamard Expansions and Hyperasymptotic Evaluation : an Extension of the Method of Steepest Descents /
"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...
| Call Number: | Libro Electrónico |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Cambridge ; New York :
Cambridge University Press,
2011, ©2011.
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| Series: | Encyclopedia of mathematics and its applications ;
v. 141. |
| Subjects: | |
| Online Access: | Texto completo |
| Summary: | "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"-- |
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| Physical Description: | 1 online resource (viii, 243 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 235-240) and index. |
| ISBN: | 9781107089853 1107089859 9780511753626 0511753624 9781107096134 1107096138 9781107101722 1107101727 1139887246 9781139887243 1107104165 9781107104167 1107093066 9781107093065 |