Exponentially accurate uniform asymptotic approximations for integrals and Bleistein's method revisited

Sarah Farid Khwaja, Adri Olde Daalhuis

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain new uniform asymptotic approximations for integrals with a relatively exponentially small remainder. We illustrate how these results can be used to obtain remainder estimates in the Bleistein method. The method is created to deal with new types of integrals in which the usual methods for remainder estimates fail. As an application, we obtain an asymptotic expansion for as in |ph λ|≤π/2 uniformly for large |z|.
Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume469
Issue number2153
Early online date6 Mar 2013
DOIs
Publication statusPublished - 8 May 2013

Keywords

  • uniform asymptotics
  • exponential asymptotics
  • Bleistein method
  • hypergeometric function

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