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.

引用

页码：161 / 164

页数：4