TY  - BOOK
AU  - Paris,R.B.
TI  - Hadamard Expansions and Hyperasymptotic Evaluation: an Extension of the Method of Steepest Descents 
T2  - Encyclopedia of mathematics and its applications
SN  - 9780511753626 (ebook)
AV  - QA431 .P287 2011
U1  - 515/.45 22
PY  - 2011///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Integral equations
KW  - Asymptotic theory
KW  - Asymptotic expansions
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511753626
ER  -