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

Describes a new asymptotic method of high-precision evaluation of certain integrals, related to the classical method of steepest descents.

R. B. Paris (Author)

9781107002586, Cambridge University Press

Hardback, published 24 March 2011

252 pages, 70 b/w illus. 30 tables
24 x 16 x 1.7 cm, 0.53 kg

"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

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]