An asymptotic expansion for the Stieltjes constants

R. B. Paris

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    Abstract

    The Stieltjes constants γn appear in the coefficients in the Laurent expansion of the Riemann zeta function ζ(s) about the simple pole s = 1. We present an asymptotic expansion for γn as n → ∞ based on the approach described by Knessl and Coffey [Math. Comput. 80 (2011) 379–386]. A truncated form of this expansion with explicit coefficients is also given. Numerical results are presented that illustrate the accuracy achievable with our expansion.
    Original languageEnglish
    Pages (from-to)707-716
    Number of pages10
    JournalMathematica Æterna
    Volume5
    Issue number5
    Publication statusPublished - 2015

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