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Exponential Asymptotics

Part of the Lecture Notes in Mathematics book series (LNM,volume 1817)

Abstract

Recently, there has been a surge of practical and theoretical interest on the part of mathematical physicists, classical analysts and abstract analysts in the subject of exponential asymptotics, or hyperasymptotics, by which is meant asymptotic approximations in which the error terms are relatively exponentially small. Such approximations generally yield much greater accuracy than classical asymptotic expansions of Poincaré type, for which the error terms are algebraically small: in other words, they lead to “exponential improvement.” They also enjoy greater regions of validity and yield a deeper understanding of other aspects of asymptotic analysis, including the Stokes phenomenon.

Keywords

  • Saddle Point
  • Asymptotic Expansion
  • Integral Representation
  • Steep Ascent
  • Divergent Series

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2003 Springer-Verlag Berlin Heidelberg

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Daalhuis, A.B.O. (2003). Exponential Asymptotics. In: Koelink, E., Van Assche, W. (eds) Orthogonal Polynomials and Special Functions. Lecture Notes in Mathematics, vol 1817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44945-0_6

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  • DOI: https://doi.org/10.1007/3-540-44945-0_6

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  • Print ISBN: 978-3-540-40375-3

  • Online ISBN: 978-3-540-44945-4

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