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Applied Mathematics and Computation
Article
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arXiv.org e-Print Archive
Preprint . 2010
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Applied Mathematics and Computation
Article . 2011 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2010
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Applied Mathematics and Computation
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Sharp bounds for harmonic numbers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2011Embargo end date: 01 Jan 2010 English Publisher:Elsevier BVJournal:Applied Mathematics and Computation, volume 218, pages 991-995 (issn: 0096-3003, Copyright policy )
Authors: Bai-Ni Guo; Feng Qi;

doi: 10.1016/j.amc.2011.01.089 , 10.48550/arxiv.1002.3856

arXiv: http://arxiv.org/abs/1002.3856

Sharp bounds for harmonic numbers

Abstract

In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double inequality -\frac{1}{12n^2+{2(7-12��)}/{(2��-1)}}\le H(n)-\ln n-\frac1{2n}-��

7 pages

Related Organizations
Keywords

Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 26D15, 33B15

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
24
Average
Top 10%
Top 10%
Green
bronze