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.
General
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