Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
From MaRDI portal
Publication:1958649
DOI10.1007/s11590-009-0173-2zbMath1225.33006OpenAlexW1972355473MaRDI QIDQ1958649
Publication date: 4 October 2010
Published in: Optimization Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11590-009-0173-2
monotonicitygamma functioninequalitiesvolume of the unit \(n\)-dimensional ballsurface area of the unit \(n\)-dimensional ball
Related Items (24)
New bounds and asymptotic expansions for the volume of the unit ball in \(\mathbb{R}^n\) based on Padé approximation ⋮ Estimates of the function and quotient by Minc-Sathre ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Topics in Special Functions III ⋮ Monotonicity and logarithmic convexity relating to the volume of the unit ball ⋮ On a determinant involving the volume of the unit ball in ⋮ The proof of Muqattash-Yahdi conjecture ⋮ Ramanujan formula for the generalized Stirling approximation ⋮ The asymptotic series of the generalized Stirling formula ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ Sharp inequalities related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ A new Stirling series as continued fraction ⋮ On Ramanujan's large argument formula for the gamma function ⋮ On the monotonicity and convexity of the remainder of the Stirling formula ⋮ A completely monotonic function used in an inequality of Alzer ⋮ Inequalities for the volume of the unit ball in \(\mathbb R^n\) ⋮ Refinements of Gurland's formula for pi ⋮ Series associated to some expressions involving the volume of the unit ball and applications ⋮ Inequalities and asymptotic expansions related to the volume of the unit ball in \(\mathbb{R}^n\) ⋮ A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in $n$-space ⋮ New improvements of the Stirling formula ⋮ ON THE INEQUALITIES FOR THE VOLUME OF THE UNIT BALL Ω_n IN R^n ⋮ Maximal volumes of \(n\)-dimensional balls in the \(p\)-norm ⋮ Some inequalities for the volume of the unit ball
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sharp inequalities and complete monotonicity for the Wallis ratio
- Improved convergence towards generalized Euler-Mascheroni constant
- A class of integral approximations for the factorial function
- An inequality for ratios of gamma functions
- An ultimate extremely accurate formula for approximation of the factorial function
- New approximations of the gamma function in terms of the digamma function
- The simplex method. A probabilistic analysis
- Special functions of quasiconformal theory
- Inequalities for the volume of the unit ball in \(\mathbb{R}^n\)
- Best estimates of the generalized Stirling formula
- Sharp inequalities related to Gosper's formula
- Inequalities for the volume of the unit ball in \(\mathbb{R}^n\). II
- Product Approximations via Asymptotic Integration
- OPTIMIZING THE RATE OF CONVERGENCE IN SOME NEW CLASSES OF SEQUENCES CONVERGENT TO EULER'S CONSTANT
- Very accurate estimates of the polygamma functions
- A monotoneity property of the gamma function
- Some properties of the gamma and psi functions, with applications
- On some inequalities for the gamma and psi functions
This page was built for publication: Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
