Optimal Lehmer mean bounds for the Toader mean
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Publication:1930326
DOI10.1007/s00025-010-0090-9zbMath1259.26035OpenAlexW2066634132MaRDI QIDQ1930326
Publication date: 10 January 2013
Published in: Results in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00025-010-0090-9
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Monotonicity theorems and inequalities for the complete elliptic integrals
- Über Lehmers Mittelwertfamilie. (On Lehmer's family of means)
- Some mean values related to the arithmetic-geometric mean
- Remark on inequalities between Hölder and Lehmer means
- Hölder means, Lehmer means, and \(x^{-1} \log \cosh x\)
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