Exponential Asymptotics

Sue Cheun Roderick WONG

Research output: Chapters, Conference Papers, Creative and Literary WorksRGC 32 - Refereed conference paper (with host publication)peer-review

Abstract

Significant developments have occurred recently in the general theory of asymptotic expansions. These developments include smoothing of the Stokes phenomenon (M. V. Berry), uniform exponentially-improved asymptotic expansions (F. W. J. Olver), superasymptotics and hyperasymp- totics (M. V. Berry and C. J. Howls). In this lecture, I will use the Airy function to give a flavor of each of these new concepts in what is now known as “exponential asymptotics” or “asymptotics beyond all orders” (M. D. Kruskal and H. Segur). My approach is based on a modified version of the steepest-descent method introduced by Berry and Howls in 1991.
Original languageEnglish
Title of host publicationSpecial Functions 2000: Current Perspective and Future Directions
Subtitle of host publicationSeries II: Mathematics, Physics and Chemistry
EditorsJoaquin Bustoz, Mourad E. H. Ismail , Sergei K. Suslov
PublisherSpringer Netherlands
Pages505-518
ISBN (Electronic)978-94-010-0818-1
ISBN (Print)978-0-7923-7120-5
DOIs
Publication statusPublished - 2001

Publication series

NameNATO Science Series
Volume30

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