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  3. Hadamard Expansions and Hyperasymptotic Evaluation
  • Cited by 15
Publisher:
Cambridge University Press
Online publication date:
March 2013
Print publication year:
2011
Online ISBN:
9780511753626
DOI:
https://doi.org/10.1017/CBO9780511753626
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
Encyclopedia of Mathematics and its Applications (141)
Information

Book description

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.

Reviews

"The book is very carefully typeset with numerous high-quality figures and numerical tables that are very helpful for following the argument for assessing the derivation, usage and accuracy of these expansions."
Gabriel Alvarez, Mathematical Reviews

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Contents

Contents
References
References
References
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