Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents (Encyclopedia of Mathematics and its Applications, Series Number 141) 1st Edition by R. B. Paris (PDF)

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.

User’s Reviews

Editorial Reviews: Review “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 Book Description Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents. About the Author R. B. Paris is a Reader in Mathematics in the Division of Complex Systems at the University of Abertay, Dundee. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this book after using the author’s previous book on asymptotics (Paris and Kaminski, “Asymptotics and Mellin-Barnes Integrals,”

⭐also an excellent book). This new effort starts with the basics of asymptotic evaluation of integrals using stationary phase and steepest descent. Several examples, in increasing order of complexity, are used to illustrate the methods. I think the level of detail provided is very appropriate for someone with a background in complex analysis who wants to learn this material by self study.The author then turns to the very recent material on hyperasymptotic expansions. This is the clearest exposition of these techniques that I have seen. Again, the amount of detail provided is just right. My current research has led me to the need to understand these techniques, and I find that this book, in conjunction with the earlier book on Mellin Transforms mentioned above, has given me what I need to use these methods. This is one of the clearest and most well-written applied math books that I’ve encountered.

⭐

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Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents (Encyclopedia of Mathematics and its Applications, Series Number 141) 1st Edition PDF Free Download
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Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents (Encyclopedia of Mathematics and its Applications, Series Number 141) 1st Edition 2011 PDF Free Download
Download Hadamard Expansions and Hyperasymptotic Evaluation: An Extension of the Method of Steepest Descents (Encyclopedia of Mathematics and its Applications, Series Number 141) 1st Edition PDF
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