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

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

9781107002586
9781107101722 (electronic book)

Cambridge ; New York : Cambridge University Press, 2011.

English

viii, 243 p. : ill.

QA431 .P287 2011

515/.45

"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.

Includes bibliographical references (p. 235-240) and index.

Access limited to authorized users.

Encyclopedia of mathematics and its applications ; v. 141.

Online Resources > Ebooks
All Resources