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Asymptotic Methods in Analysis

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Analysis I

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 13))

Abstract

An asymptotic formula or asymptotic form for a function f(x) is the name usually given to an approximate formula f(x) ≈ g(x) in some domain of values of x, where g(x) is ‘simpler’ then f(x). For example, if f(x) is an integral, then g(x) must either be given in terms of the values of the integrand and its derivatives at a finite number of points, or in terms of some simpler integral. If f(x) is a solution of an ordinary differential equation, then g(x) must either be expressed in quadratures or be the solution of a ‘simpler’ differential equation. This list can be extended—there is an unwritten heirarchy of asymptotic formulae. Of course all these definitions are very blurred. ‘“What is asymptotics?” This question is about as difficult to answer as the question “What is mathematics?”’

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Authors
  1. M. V. Fedoryuk
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Editors and Affiliations

  1. Academy of Sciences of the USSR, Steklov Mathematical Institute, ul. Vavilova 42, 117966, Moscow, USSR

    R. V. Gamkrelidze

  2. Institute for Scientific Information (VINITI), Baltiiskaya ul. 14, 125219, Moscow, USSR

    R. V. Gamkrelidze

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© 1989 Springer-Verlag Berlin Heidelberg

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Fedoryuk, M.V. (1989). Asymptotic Methods in Analysis. In: Gamkrelidze, R.V. (eds) Analysis I. Encyclopaedia of Mathematical Sciences, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61310-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-61310-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64786-4

  • Online ISBN: 978-3-642-61310-4

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