On the Ramanujan–Lodge harmonic number expansion

作者：

Highlights：

•

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.

论文关键词：Harmonic numbers,Bernoulli numbers,Asymptotic expansion,Rate of convergence,Approximations,Inequalities

论文评审过程：Available online 12 December 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.11.088