Asymptotic Approximations of Integrals [First ed.] 0-12-762535-6, 9780127625355, 9781483220710, 1483220710

Table of contents :
Content: Front Cover
Asymptotic Approximations of Integrals
Copyright Page
Dedication
Table of Contents
Preface
Chapter I. Fundamental Concepts ofAsymptotics
1. What Is Asymptotics?
2. Asymptotic Expansions
3. Generalized Asymptotic Expansions
4. Integration by Parts
5. Watson's Lemma
6. The Euler-Maclaurin Summation Formula
Exercises
Supplementary Notes
Chapter II. Classical Procedures
1. Laplace's Method
2. Logarithmic Singularities
3. The Principle of Stationary Phase
4. Method of Steepest Descents
5. Perron's Method
6. Darboux's Method
7. A Formula of Hayman
Exercises. Supplementary NotesChapter III. Mellin Transform Techniques
1. Introduction
2. Properties of Mellin Transforms
3. Examples
4. Work of Handelsman and Lew
5. Remarks and Examples
6. Explicit Error Terms
7. A Double Integral
Exercises
Supplementary Notes
SHORT TABLE OF MELLIN TRANSFORMS
Chapter IV. The Summability Method
1. Introduction
2. A Fourier Integral
3. Hankel Transform
4. Hankel Transform (continued)
5. Oscillatory Kernels: General Case
6. Some Quadrature Formulas
7. Mellin-Barnes Type Integrals
Exercises
Supplementary Notes. 4. Hilbert Transforms5. Laplace and Fourier Transforms Near the Origin
6. Fractional Integrals
7. The Method of Regularization
Exercises
Supplementary Notes
Chapter VII. Uniform AsymptoticExpansions
1. Introduction
2. Saddle Point near a Pole
3. Saddle Point near an Endpoint
4. Two Coalescing Saddle Points
5. Laguerre Polynomials I
6. Many Coalescing Saddle Points
7. Laguerre Polynomials II
8. LegendreFunction
Exercises
Supplementary Notes
Chapter VIII. Double Integrals
1. Introduction
2. Classification of Critical Points
3. Local Extrema
4. Saddle Points. 5. A Degenerate Case6. Boundary Stationary Points
7. Critical Points of the Second Kind
8. Critical Points of the Third Kind
9. A Curve of Stationary Points
10. Laplace's Approximation
11. Boundary Extrema
Exercises
Supplementary Notes
Chapter IX. Higher DimensionalIntegrals
1. Introduction
2. Stationary Points
3. Points of Tangential Contact
4. Degenerate Stationary Point
5. Laplace's Approximation inRn
6. Multiple Fourier Transforms
Exercises
Supplementary Notes
Bibliography
Symbol Index
Author Index
Subject Index.

Polecaj historie

Asymptotic Expansions of Integrals [Reprinted Edition] 0486650820

Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits,

675 124 16MB Read more

Theory and numerical approximations of fractional integrals and derivatives

1,259 93 2MB Read more

Non-Asymptotic Analysis of Approximations for Multivariate Statistics [1st ed.] 9789811326158, 9789811326165

This book presents recent non-asymptotic results for approximations in multivariate statistical analysis. The book is un

313 45 2MB Read more

Theory and numerical approximations of fractional integrals and derivatives 9781611975871, 1611975875

"This book provides a comprehensive review of fractional calculus, covering both theory and numerical methods, and

1,429 78 5MB Read more

Stochastic equations through the eye of the physicist basic concepts, exact results and asymptotic approximations 0444517979, 9780444517975, 9780080457642

Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random force

443 54 8MB Read more

Mistrust: Ethnographic Approximations 9783839439234

Scholars have long seen trust as a foundational social good. We therefore have ample studies on building trust in free m

156 99 1MB Read more

Methods of Mathematical Physics. Asymptotic Methods

This textbook presents supplementary chapters to the course “Methods of Mathematical Physics” and contains a material on

847 179 9MB Read more

Approximations and Endomorphism Algebras of Modules: Volume 1 – Approximations / Volume 2 – Predictions [2 ed.] 9783110218107, 9783110218114

This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects

186 91 7MB Read more

Normal approximations with Malliavin calculus 9781107017771

423 99 1MB Read more

Higher Approximations in Aerodynamic Theory

453 41 17MB Read more