Inequalities and asymptotic expansions related to the volume of the unit ball in \(\mathbb{R}^n\)

DOI10.1007/s00025-019-0967-1zbMath1407.33003OpenAlexW2912421211MaRDI QIDQ667582

Chao-Ping Chen, Richard B. Paris

Publication date: 28 February 2019

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-019-0967-1

zbMATH Keywords

gamma functioninequalitiesasymptotic expansionsvolume of the unit \(n\)-dimensional ball

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities for sums, series and integrals (26D15)

Related Items (2)

On a determinant involving the volume of the unit ball in ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\)

Uses Software

• DLMF

Cites Work

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• Estimates of the function and quotient by Minc-Sathre
• A new general asymptotic formula and inequalities involving the volume of the unit ball
• Monotonicity and logarithmic convexity relating to the volume of the unit ball
• Remarks on some completely monotonic functions
• Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
• The simplex method. A probabilistic analysis
• Special functions of quasiconformal theory
• Completely monotonic and related functions
• Inequalities and asymptotic expansions associated with the Ramanujan and nemes formulas for the gamma function
• Series associated to some expressions involving the volume of the unit ball and applications
• Inequalities for the volume of the unit ball in \(\mathbb{R}^n\)
• Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
• Inequalities for the volume of the unit ball in \(\mathbb{R}^n\). II
• Inequalities for the volume of the unit ball in \(\mathbb R^n\)
• Gurland's ratio for the gamma function
• The special functions and their approximations. Vol. I, II
• Asymptotic formulae associated with the Wallis power function and digamma function
• Some inequalities for the volume of the unit ball
• A monotoneity property of the gamma function
• New inequalities for the volume of the unit ball in ℝ^n
• On some inequalities for the gamma and psi functions

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