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.
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页码：9755 / 9761
页数：7
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