Addison-type series representation for the Stieltjes constants

JOURNAL OF NUMBER THEORY

卷:130

Article

Coffey, Mark W.

关键词: Stieltjes constants;    Riemann zeta function;    Laurent expansion;    Series representation;    Hurwitz zeta function;   

DOI  :  10.1016/j.jnt.2010.01.003

来源: Elsevier

【 摘 要 】

The Stieltjes constants gamma(k)(a) appear in the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function zeta(s, a) about its only pole at s = 1. We generalize a technique of Addison for the Euler constant gamma = gamma(0)(1) to show its application to finding series representations for these constants. Other generalizations of representations of gamma are given. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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