Asymptotic approximations of integrals

Society for Industrial and Applied Mathematics

2001

xvii, 543 p.

Classics in applied mathematics ; 34

Includes bibliographical references (p. 517-532) and indexes

9780898714975

Fundamental concepts of asymptotics -- Classical procedures -- Mellin transform techniques -- The summability method -- Elementary theory of distributions -- The distributional approach -- Uniform asymptotic expansions -- Double integrals -- Higher dimensional integrals

Asymptotic methods are frequently used in many branches of both pure and applied mathematics, and this classic text remains the most up-to-date book dealing with one important aspect of this area, namely, asymptotic approximations of integrals. In Asymptotic Approximations of Integrals, all results are proved rigorously, and many of the approximation formulas are accompanied by error bounds. A thorough discussion on multidimensional integrals is given, and references are provided. The book contains the "distributional method," which is not available elsewhere. Most of the examples in this text come from concrete applications. Since its publication twelve years ago, significant developments have occurred in the general theory of asymptotic expansions, including smoothing of the Stokes phenomenon, uniform exponentially improved asymptotic expansions, and hyperasymptotics. These new concepts belong to the area now known as "exponential asymptotics." Expositions of these new theories are available in papers published in various journals, but not yet in book form. Audience: this book can be used either as a text for graduate students in mathematics, physics, and engineering or as a reference for research workers in these fields

Английский