Asymptotic Expansions of Integrals

Author: Norman Bleistein,Richard A. Handelsman

Publisher: Courier Corporation

ISBN: 0486650820

Category: Mathematics

Page: 425

View: 7792

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Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
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Asymptotic Expansions

Author: E. T. Copson,Edward Thomas Copson

Publisher: Cambridge University Press

ISBN: 9780521604826

Category: Mathematics

Page: 120

View: 5888

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Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
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Asymptotic Approximations of Integrals

Computer Science and Scientific Computing

Author: R. Wong

Publisher: Academic Press

ISBN: 1483220710

Category: Mathematics

Page: 556

View: 2966

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Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.
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Asymptotic Expansions of Integrals

Author: Norman Bleistein,Richard A. Handelsman

Publisher: Ardent Media

ISBN: 9780030835964

Category: Mathematics

Page: 425

View: 7651

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Coherent, systematic coverage of standard methods: integration by parts, Watson's lemma, LaPlace's method, stationary phase and steepest descents. Also includes Mellin transform method and less elementary aspects of the method of steepest descents. Abundant exercises. 1975 edition.
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Asymptotic Expansions

Author: A. Erdélyi

Publisher: Courier Corporation

ISBN: 0486155056

Category: Mathematics

Page: 128

View: 2665

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Various methods for asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansion.
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Asymptotic Expansion of Multiple Integrals and the Method of Stationary Phase

Author: Douglas S Jones,Morris Kline

Publisher: Franklin Classics

ISBN: 9780343131647

Category:

Page: 54

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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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Asymptotic Expansion of a Partition Function Related to the Sinh-model

Author: Gaëtan Borot,Alice Guionnet,Karol K. Kozlowski

Publisher: Springer

ISBN: 3319333798

Category: Science

Page: 222

View: 2041

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This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
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