A new upper bound in the second Kershaw's double inequality and its generalizations

DOI10.1016/j.cam.2007.07.037zbMath1149.26026OpenAlexW2082383656MaRDI QIDQ939514

Feng Qi, Shou-Xin Chen, Sen-Lin Guo

Publication date: 22 August 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2007.07.037

zbMATH Keywords

upper boundextensiongeneralizationrefinementdivided differencecompletely monotonic functionpsi functionidentric meanpolygamma functionlogarithmically completely monotonic functionratio of gamma functionsgeneralized logarithmic meanexponential meanKershaw's double inequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other analytical inequalities (26D20) Inequalities involving other types of functions (26D07)

Related Items (9)

An inequality involving the gamma and digamma functions ⋮ Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions ⋮ Complete monotonicity of some functions involving polygamma functions ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ Random Double Tensors Integrals ⋮ The harmonic and geometric means are Bernstein functions ⋮ Schur \(m\)-power convexity for general geometric Bonferroni mean of multiple parameters and comparison inequalities between several means ⋮ Bounds for the ratio of two gamma functions ⋮ Some properties of the Fuss-Catalan numbers

Cites Work

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• Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• On Gamma Function Inequalities
• The best bounds in Gautschi's inequality
• Three classes of logarithmically completely monotonic functions involving gamma and psi functions
• Some completely monotonic functions involving the gamma and polygamma functions
• What is the Laplace Transform?

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