An asymptotic expansion for the Stieltjes constants

R. B. Paris

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 language	English
Pages (from-to)	707-716
Number of pages	10
Journal	Mathematica Æterna
Volume	5
Issue number	5
Publication status	Published - 2015

Keywords

Stieltjes constants
Laurent expansion
Asymptotic expansion

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AB - 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.

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JO - Mathematica Æterna

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An asymptotic expansion for the Stieltjes constants

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