A new general asymptotic formula and inequalities involving the volume of the unit ball

DOI10.1016/j.jnt.2016.06.010zbMath1420.40002OpenAlexW2502278703MaRDI QIDQ311476

Peixuan Zhang, Dawei Lu

Publication date: 13 September 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.06.010

zbMATH Keywords

gamma functioninequalitiesrate of convergenceasymptotic formulacontinued fractionthe volume of the unit \(n\)-dimensional ball

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Length, area, volume, other geometric measure theory (28A75) Approximation to limiting values (summation of series, etc.) (40A25)

Related Items (3)

New bounds and asymptotic expansions for the volume of the unit ball in \(\mathbb{R}^n\) based on Padé approximation ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ Inequalities and asymptotic expansions related to the volume of the unit ball in \(\mathbb{R}^n\)

Cites Work

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• Inequalities for the volume of the unit ball in \(\mathbb R^n\)
• Product Approximations via Asymptotic Integration
• A monotoneity property of the gamma function
• On some inequalities for the gamma and psi functions

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