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Hadamard Expansions and Hyperasymptotic Evaluation
An Extension of the Method of Steepest Descents


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: March 2011
  • availability: Available
  • format: Hardback
  • isbn: 9781107002586


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About the Authors
  • 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.

    • Presents a brand new method useful for high-precision evaluation
    • Includes a detailed account of the classical method with examples and cases of breakdown due to coalescence problems
    • Illustrated with many numerical examples
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    Product details

    • Date Published: March 2011
    • format: Hardback
    • isbn: 9781107002586
    • length: 252 pages
    • dimensions: 240 x 160 x 17 mm
    • weight: 0.53kg
    • contains: 70 b/w illus. 30 tables
    • availability: Available
  • Table of Contents

    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

  • Author

    R. B. Paris, University of Abertay, Dundee
    R. B. Paris is a Reader in Mathematics in the Division of Complex Systems at the University of Abertay, Dundee.

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