Sharp bounds for harmonic numbers

DOI10.1016/j.amc.2011.01.089zbMath1229.11027arXiv1002.3856OpenAlexW2144784366MaRDI QIDQ648251

Bai-Ni Guo, Feng Qi

Publication date: 22 November 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.3856

zbMATH Keywords

inequalitypsi functionharmonic numbersharp bound

Mathematics Subject Classification ID

Farey sequences; the sequences (1^k, 2^k, dots) (11B57)

Related Items (14)

Optimal bounds for the generalized Euler-Mascheroni constant ⋮ Monotonicity rules for the ratio of two Laplace transforms with applications ⋮ Dynamic Fair Resource Division ⋮ Are random permutations spherically uniform? ⋮ Zip-zip trees: making zip trees more balanced, biased, compact, or persistent ⋮ Sharp bounds for harmonic numbers ⋮ Action of generalized symmetric groups on symmetric and exterior powers of their natural representations ⋮ Complete monotonicity of a function involving the gamma function and applications ⋮ Continued fraction estimates for the psi function ⋮ Monotonicity properties and inequalities related to generalized Grötzsch ring functions ⋮ Inequalities and asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Several series identities involving the Catalan numbers ⋮ Extreme Value Analysis for Progressively Type-II Censored Order Statistics ⋮ Necessary and sufficient conditions for functions involving the psi function to be completely monotonic

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• Sharp inequalities for the psi function and harmonic numbers
• Some completely monotonic functions involving polygamma functions and an application
• Some properties of the psi and polygamma functions
• 75.9 Euler’s Constant
• On some inequalities for the gamma and psi functions

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