Sharp, double inequalities bounding the function (1+x)^(1/x) and a refinement of Carleman's inequality

DOI10.7153/MIA-2023-26-08OpenAlexW4322580825MaRDI QIDQ5881769

Durvudkhan Suragan

Publication date: 13 March 2023

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-2023-26-08

zbMATH Keywords

monotonicityexponential functionexpansionapproximationestimatesequencenumber \(e\)double inequality

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by other special function classes (41A30) Other analytical inequalities (26D20)

Uses Software

• Unnamed Item

Cites Work

• Continued fraction inequalities related to \((1+\frac{1}{x})^x\)
• On Hardy's inequality
• On an infinite series for \((1 + 1/x)^{x}\) and its application
• Approximation formulas for the constant \(e\) and an improvement to a Carleman-type inequality
• A best approximation for constant \(e\) and an improvement to Hardy's inequality
• Padé approximant related to inequalities involving the constant \(e\) and a generalized Carleman-type inequality
• New strengthened Carleman's inequality and Hardy's inequality
• On some convergences to the constant e and improvements of Carlemans' inequality
• An Asymptotic Formula for (1 + 1/<em>x</em>)<em>^x</em> Based on the Partition Function
• Asymptotic Formula for (1 + 1/<em>x</em>)^<em>x</em>, Revisited
• On strengthened weighted Carleman's inequality
• An inequality involving the constant e and a generalized Carleman-type inequality
• Estimates of (1+x)1/x involved in Carleman’s inequality and Keller’s limit

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