Asymptotic Expansions of Integrals

Asymptotic Expansions of Integrals
Author: Norman Bleistein
Publisher: Courier Corporation
Total Pages: 453
Release: 1986-01-01
Genre: Mathematics
ISBN: 0486650820

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.

Asymptotic Expansions for Ordinary Differential Equations

Asymptotic Expansions for Ordinary Differential Equations
Author: Wolfgang Wasow
Publisher: Courier Dover Publications
Total Pages: 385
Release: 2018-03-21
Genre: Mathematics
ISBN: 0486824586

This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Matched Asymptotic Expansions

Matched Asymptotic Expansions
Author: P.A. Lagerstrom
Publisher: Springer Science & Business Media
Total Pages: 263
Release: 2013-03-09
Genre: Mathematics
ISBN: 1475719906

Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.

Asymptotic Expansions

Asymptotic Expansions
Author: A. Erdélyi
Publisher: Courier Corporation
Total Pages: 118
Release: 1956-01-01
Genre: Mathematics
ISBN: 0486603180

Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.

Asymptotic Expansions

Asymptotic Expansions
Author: E. T. Copson
Publisher: Cambridge University Press
Total Pages: 136
Release: 2004-06-03
Genre: Mathematics
ISBN: 9780521604826

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

Applied Asymptotic Expansions in Momenta and Masses

Applied Asymptotic Expansions in Momenta and Masses
Author: Vladimir A. Smirnov
Publisher: Springer
Total Pages: 265
Release: 2014-03-12
Genre: Science
ISBN: 9783662146590

'The sturgeon they sent was second grade fresh,' said the barman. 'Really, what nonsense/' 'Why nonsense?' '"Second grade fresh" that's what I call nonsense/ There's only one degree of freshness the first, and it's the last) (M. A. Bulgakov, The Master and Margarita) The goal of this book is to describe in detail how Feynman integrals can be expanded in suitable parameters, when various momenta or masses are small or large. In a narrow sense, this problem is connected with practical calcula tions. In a situation where a given Feynman integral depends on parameters of very different scales, a natural idea is to replace it by a sufficiently large number of terms of an expansion of it in ratios of small and large scales. It will be explained how this problem of expansion can be systematically solved, by formulating universal prescriptions that express terms of the expansion by using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. It turns out that knowledge of the structure of the asymptotic expansion at the diagrammatic level is a key point in understanding how to perform expansions at the operator level. There are various examples of these ex pansions: the operator product expansion, the large mass expansion, Heavy Quark Effective Theory, Non Relativistic QCD, etc. Each of them serves as a realization of the factorization of contributions of different scales.

Asymptotic Approximations of Integrals

Asymptotic Approximations of Integrals
Author: R. Wong
Publisher: Academic Press
Total Pages: 561
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483220710

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.

Asymptotic Expansion of a Partition Function Related to the Sinh-model

Asymptotic Expansion of a Partition Function Related to the Sinh-model
Author: Gaëtan Borot
Publisher: Springer
Total Pages: 233
Release: 2016-12-08
Genre: Science
ISBN: 3319333798

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.