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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Asymptotic Expansion
Laurent Expansion
Coefficient
Riemann zeta function
Pole
Numerical Results
Form

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Paris, R. B. / An asymptotic expansion for the Stieltjes constants. In: Mathematica Æterna. 2015 ; Vol. 5, No. 5. pp. 707-716.
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Paris, RB 2015, 'An asymptotic expansion for the Stieltjes constants', Mathematica Æterna, vol. 5, no. 5, pp. 707-716.

An asymptotic expansion for the Stieltjes constants. / Paris, R. B.

In: Mathematica Æterna, Vol. 5, No. 5, 2015, p. 707-716.

Research output: Contribution to journal › Article

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T1 - An asymptotic expansion for the Stieltjes constants

AU - Paris, R. B.

PY - 2015

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N2 - 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.

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.

M3 - Article

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JF - Mathematica Æterna

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Paris RB. An asymptotic expansion for the Stieltjes constants. Mathematica Æterna. 2015;5(5):707-716.

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