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Asymptotic approximations of integrals /

Asymptotic Approximations of Integrals.

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Bibliographic Details
Main Authors: Wong, Roderick, 1944- (Author)
Corporate Authors: Elsevier Science & Technology.
Published: Academic Press,
Publisher Address: Boston :
Publication Dates: 1989.
Literature type: eBook
Language: English
Series: Computer science and scientific computing
Subjects:
Integrals.
Approximation theory.
Asymptotic expansions.
transformation Mellin.
Transformation Hankel.
Transformation Stieltjes.
Transformation Hilbert.
Inte grale multiple.
Lemme Watson.
Formule sommation Euler-MacLaurin.
Inte grale Mellin-Barnes.
Inte grales.
The orie de l'approximation.
De veloppements asymptotiques.
Approximation, The orie de l'
approximation.
Asymptotische Methode
Integral.
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Electronic books.
Online Access: http://www.sciencedirect.com/science/book/9780127625355
Summary: Asymptotic Approximations of Integrals.
Item Description: Includes indexes.
Carrier Form: 1 online resource (xiii, 544 pages) : illustrations.
Bibliography: Includes bibliographical references (pages 517-532).
ISBN: 9781483220710
1483220710
Index Number: QA311
CLC: O172.2
Contents: 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.

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