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arXiv.org e-Print Archive
Preprint . 2009
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Article . 2014 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2009
License: arXiv Non-Exclusive Distribution
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https://arxiv.org/pdf/0902.252...
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Sharp inequalities for the psi function and harmonic numbers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 28 Jan 2014Embargo end date: 01 Jan 2009Publisher:Walter de Gruyter GmbHJournal:Analysis, volume 34 (issn: 0174-4747, eissn: 2196-6753, Copyright policy )
Authors: Bai-Ni Guo; Feng Qi;

doi: 10.1515/anly-2014-0001 , 10.48550/arxiv.0902.2524

arXiv: http://arxiv.org/abs/0902.2524

Sharp inequalities for the psi function and harmonic numbers

Abstract

In this paper, two sharp inequalities for bounding the psi function $��$ and the harmonic numbers $H_n$ are established respectively, some results in [I. Muqattash and M. Yahdi, \textit{Infinite family of approximations of the Digamma function}, Math. Comput. Modelling \textbf{43} (2006), 1329\nobreakdash--1336.] are improved, and some remarks are given.

6 pages, 2 figures

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Keywords

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

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    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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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!
35
Top 10%
Top 10%
Top 10%
Green
bronze