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

共 50 条

[1] Inequalities for the Euler-Mascheroni constant
Chen, Chao-Ping
APPLIED MATHEMATICS LETTERS, 2010, 23 (02) : 161 - 164
[2] IMPROVING SOME INEQUALITIES ASSOCIATED WITH THE EULER-MASCHERONI CONSTANT
Cringanu, Jenica
JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (03): : 667 - 673
[3] On the Euler-Mascheroni constant
Macys, J. J.
MATHEMATICAL NOTES, 2013, 94 (5-6) : 647 - 652
[4] Approximation formulas and inequalities for the Euler-Mascheroni constant
Chao-Ping Chen
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021, 115
[5] Continued fraction inequalities for the Euler-Mascheroni constant
Xu, Hongmin
You, Xu
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[6] EULER-MASCHERONI CONSTANT
BARNES, ER
KAUFMAN, WE
CHESSIN, PL
GOLDBERG, M
HANSEN, E
ZEITLIN, D
AMERICAN MATHEMATICAL MONTHLY, 1965, 72 (09): : 1023 - &
[7] Continued fraction inequalities for the Euler-Mascheroni constant
Hongmin Xu
Xu You
Journal of Inequalities and Applications, 2014
[8] Approximation formulas and inequalities for the Euler-Mascheroni constant
Chen, Chao-Ping
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2021, 115 (02)
[9] On the Euler-Mascheroni constant
J. J. Mačys
Mathematical Notes, 2013, 94 : 647 - 652
[10] FORMULAS FOR THE EULER-MASCHERONI CONSTANT
Panzone, Pablo A.
REVISTA DE LA UNION MATEMATICA ARGENTINA, 2009, 50 (01): : 161 - 164

← 1 2 3 4 5 →