Asymptotics of the Mittag-Leffler function Ea(z) on the negative real axis when a→1

Richard Paris*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider the asymptotic expansion of the one-parameter Mittag-Leffler functionEa(−x) for x → +∞ as the parameter a → 1. The dominant expansion when0 < a < 1 consists of an algebraic expansion of O(x−1) (which vanishes whena = 1), together with an exponentially small contribution that approaches e−x as a → 1. Here we concentrate on the form of this exponentially small expansion whena approaches the value 1. Numerical examples are presented to illustrate the accuracyof the expansion so obtained.
    Original languageEnglish
    Pages (from-to)735-746
    Number of pages12
    JournalFractional Calculus and Applied Analysis
    Volume25
    Issue number2
    Early online date20 Apr 2022
    DOIs
    Publication statusPublished - 20 Apr 2022

    Keywords

    • Mittag-Leffler function
    • Asymptotic expansion
    • Exponentially small expansion
    • Stokes lines

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