On the Ramanujan-Lodge harmonic number expansion

被引：16

作者：

Mortici, Cristinel ^{[1
,2
]}

Villarino, Mark B. ^{[3
]}

机构：

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

[2] Acad Romanian Scientists, Bucharest 050094, Romania

[3] Univ Costa Rica, Dept Math, San Jose, Costa Rica

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 251卷

关键词：

Harmonic numbers; Bernoulli numbers; Asymptotic expansion; Rate of convergence; Approximations; Inequalities; APPROXIMATIONS;

D O I：

10.1016/j.amc.2014.11.088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to extend and refine the Ramanujan-Lodge harmonic number expansion into negative powers of a triangular number. We construct a faster asymptotic series and some new sharp inequalities for the harmonic numbers. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：423 / 430

页数：8

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