Limits and inequalities associated with the Euler-Mascheroni constant

被引：5

作者：

Chen, Chao-Ping ^{[1
]}

Mortici, Cristinel ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454003, Henan Province, Peoples R China

[2] Valahia Univ Targoviste, Dept Math, Targoviste 130082, Romania

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 18期

关键词：

Euler-Mascheroni constant; Harmonic numbers; Inequality; Psi function; Polygamma functions; Asymptotic expansion; GAMMA; CONVERGENCE;

D O I：

10.1016/j.amc.2013.03.089

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

i) We present several limits associated with the Euler-Mascheroni constant. (ii) Let gamma = 0: 577215... be the Euler-Mascheroni constant, and let T-n = Sigma(n)(k) 1/1k - ln (n+1/2+1/24n) and P-n = Sigma(n)(k-1) 2/2k-1-In (4n). We determine the best possible constants alpha,beta, a and b such that the inequalities 1/48(n+alpha)(3)<= gamma -T-n < 1/48(n+beta)(3) and 1/24(n+a)(2)<= P-n- gamma < 1/24(n+b)(2) are valid for all integers n >= 1. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：9755 / 9761

页数：7

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