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


    We consider the asymptotic expansion of the one-parameter Mittag-Leffler function Ea(−x) for x → +∞ as the parameter a → 1. The dominant expansion when 0 < a < 1 consists of an algebraic expansion of O(x−1) (which vanishes when a = 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 when a approaches the value 1. Numerical examples are presented to illustrate the accuracy of the expansion so obtained.
    Original languageEnglish
    Number of pages12
    JournalFractional Calculus and Applied Analysis
    Early online date20 Apr 2022
    Publication statusE-pub ahead of print - 20 Apr 2022


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

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