Asymptotic approximations of integrals

R. Wong9780898714975, 0898714974

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. Asymptotic Approximations of Integrals 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.

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Table of contents :
Asymptotic Approximations of Integrals……Page 1
Contents……Page 10
Preface to the Classics Edition……Page 14
Preface……Page 16
Part I: Fundamental Concepts of Asymptotics……Page 20
Part II: Classical Procedures……Page 74
Part III: Mellin Transform Techniques……Page 166
Part IV: The Summability Method……Page 214
Part V: Elementary Theory of Distributions……Page 260
Part VI: The Distributional Approach……Page 312
Part VII: Uniform Asymptotic Expansions……Page 372
Part VIII: Double Integrals……Page 442
Part IX: Higher Dimensional Integrals……Page 496
Bibliography……Page 536
Symbol Index……Page 552
Author Index……Page 554
Subject Index……Page 558