Asymptotic Expansions

Author: A. Erdélyi

Publisher: Courier Corporation

ISBN: 0486155056

Category: Mathematics

Page: 128

View: 8130

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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 Expansions of Integrals

Author: Norman Bleistein,Richard A. Handelsman

Publisher: Courier Corporation

ISBN: 0486650820

Category: Mathematics

Page: 425

View: 6123

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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

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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 Expansions: Elementary methods

Author: Johannes Gualtherus Corput,California. University. Dept. of Mathematics,University of California. Dept. of Mathematics,United States. Air Force. Air Research and Development Command

Publisher: N.A

ISBN: N.A

Category: Asymptotic expansions

Page: N.A

View: 2870

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Applied Asymptotic Expansions in Momenta and Masses

Author: Vladimir A. Smirnov

Publisher: Springer

ISBN: 3540445749

Category: Science

Page: 265

View: 1467

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'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.
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Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Corporation

ISBN: 9780486495187

Category: Mathematics

Page: 374

View: 2778

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"A book of great value . . . it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding the solutions of ordinary differential equations. Moreover, they have come to be seen as crucial to such areas of applied mathematics as quantum mechanics, viscous flows, elasticity, electromagnetic theory, electronics, and astrophysics. In this outstanding text, the first book devoted exclusively to the subject, the author concentrates on the mathematical ideas underlying the various asymptotic methods; however, asymptotic methods for differential equations are included only if they lead to full, infinite expansions. Unabridged Dover republication of the edition published by Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, a corrected, slightly enlarged reprint of the original edition published by Interscience Publishers, New York, 1965. 12 illustrations. Preface. 2 bibliographies. Appendix. Index.
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