### Abstract

Original language | English |
---|---|

Pages (from-to) | 707-716 |

Number of pages | 10 |

Journal | Mathematica Æterna |

Volume | 5 |

Issue number | 5 |

Publication status | Published - 2015 |

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*Mathematica Æterna*,

*5*(5), 707-716.

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*Mathematica Æterna*, vol. 5, no. 5, pp. 707-716.

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - An asymptotic expansion for the Stieltjes constants

AU - Paris, R. B.

PY - 2015

Y1 - 2015

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

VL - 5

SP - 707

EP - 716

JO - Mathematica Æterna

JF - Mathematica Æterna

SN - 1314-3344

IS - 5

ER -