Inequalities for the Euler-Mascheroni constant

被引：25
|
作者：
Chen, Chao-Ping [1 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454003, Henan, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 02期
关键词：
Euler's constant; Harmonic numbers; Inequality; Psi function; Asymptotic expansion; CONVERGENCE;
D O I：
10.1016/j.aml.2009.09.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let gamma = 0.577215... be the Euler-Mascheroni constant, and let R-n = Sigma(n)(k=1) 1/k - log (n + 1/2). We prove that for all integers n >= 1. 1/24(n +a)(2) <= R-n - gamma < 1/24(n + b)(2) with the best possible constants a = - 1/root 24[-gamma + 1 - log(3/2)] - 1 = 0.55106 ... and b = 1/2. This refines the result of D. W. DeTemple, who proved that the double inequality holds with a = 1 and b = 0. (C) 2009 Elsevier Ltd. All rights reserved.
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页码：161 / 164
页数：4
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