Exponential asymptotics of the Mittag-Leffler function

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • R. Wong
  • Yu-Qiu Zhao

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)355-385
Journal / PublicationConstructive Approximation
Volume18
Issue number3
Publication statusPublished - 2002

Abstract

The Stokes lines/curves are identified for the Mittag-Leffler function Eα,β(z) = Σn=0 zn/Γ(αn + β), Re α>0. When α is not real, it is found that the Stokes curves are spirals. Away from the Stokes lines/curves, exponentially improved uniform asymptotic expansions are obtained. Near the Stokes lines/curves, Berry-type smooth transitions are achieved via the use of the complementary error function.

Research Area(s)

  • Berry-type smooth transition, Exponential asymptotics, Mittag-Leffler function, Stokes lines/curves

Citation Format(s)

Exponential asymptotics of the Mittag-Leffler function. / Wong, R.; Zhao, Yu-Qiu.
In: Constructive Approximation, Vol. 18, No. 3, 2002, p. 355-385.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review