Hadamard expansions and hyperasymptotic evaluation [electronic resource] : an extension of the method of steepest descents / R.B. Paris.
2011
QA431 .P287 2011
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Title
Hadamard expansions and hyperasymptotic evaluation [electronic resource] : an extension of the method of steepest descents / R.B. Paris.
Author
Paris, R. B.
ISBN
9781107002586
9781107101722 (electronic book)
9781107101722 (electronic book)
Publication Details
Cambridge ; New York : Cambridge University Press, 2011.
Language
English
Description
viii, 243 p. : ill.
Call Number
QA431 .P287 2011
Dewey Decimal Classification
515/.45
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"-- Provided by publisher.
Bibliography, etc. Note
Includes bibliographical references (p. 235-240) and index.
Access Note
Access limited to authorized users.
Series
Encyclopedia of mathematics and its applications ; v. 141.
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Table of Contents
Machine generated contents note: Preface
1. Asymptotics of Laplace-type integrals
2. Hadamard expansion of Laplace integrals
3. Hadamard expansion of Laplace-type integrals
4. Applications
Appendix A
Appendix B
Appendix C
References
Index.
1. Asymptotics of Laplace-type integrals
2. Hadamard expansion of Laplace integrals
3. Hadamard expansion of Laplace-type integrals
4. Applications
Appendix A
Appendix B
Appendix C
References
Index.