Hadamard expansions and hyperasymptotic evaluation [electronic resource] : an extension of the method of steepest descents / R.B. Paris.

By: Paris, R. BContributor(s): ProQuest (Firm)Material type: TextTextSeries: Encyclopedia of mathematics and its applications ; v. 141.Publication details: Cambridge ; New York : Cambridge University Press, 2011Description: viii, 243 p. : illISBN: 9781107101722 (electronic bk.)Subject(s): Integral equations -- Asymptotic theory | Asymptotic expansionsGenre/Form: Electronic books.DDC classification: 515/.45 LOC classification: QA431 | .P287 2011Online resources: Click to View
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.
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.
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Includes bibliographical references (p. 235-240) and index.

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.

"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.

Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

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