Sharp inequalities for the harmonic numbers

DOI10.1016/j.exmath.2006.02.001zbMath1105.11003OpenAlexW2064717855WikidataQ60692188 ScholiaQ60692188MaRDI QIDQ860367

Horst Alzer

Publication date: 9 January 2007

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2006.02.001

zbMATH Keywords

inequalitiesharmonic numbers

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Inequalities for sums, series and integrals (26D15) Special sequences and polynomials (11B83)

Related Items

Some monotonicity properties and inequalities for the generalized digamma and polygamma functions ⋮ Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ The monotonicity and convexity of a function involving psi function with applications ⋮ Inequalities for the harmonic numbers ⋮ Complete monotonicity related to the \(k\)-polygamma functions with applications ⋮ Sharp bounds for harmonic numbers ⋮ Refinements of lower bounds for polygamma functions ⋮ On proofs for monotonicity of a function involving the psi and exponential functions ⋮ Notes on three conjectures involving the digamma and generalized digamma functions ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions

Uses Software

• OEIS

Cites Work

• A binomial coefficient identity associated with Beukers' conjecture on {A}péry numbers
• The Fifty-Eighth William Lowell Putnam Mathematical Competition
• On an Intriguing Integral and Some Series Related to ζ(4)
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