Monotonicity properties of the volume of the unit ball in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n}}$$\end{document}

被引:1
作者
Cristinel Mortici
机构
[1] Valahia University of Târgovişte,Department of Mathematics
关键词
Volume of the unit ; -dimensional ball; Surface area of the unit ; -dimensional ball; Gamma function; Monotonicity; Inequalities;
D O I
10.1007/s11590-009-0173-2
中图分类号
学科分类号
摘要
The aim of this paper is to establish new bounds for ratios involving the volume of the unit ball in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n}}$$\end{document}.
引用
收藏
页码:457 / 464
页数:7
相关论文
共 19 条
  • [1] Alzer H.(1997)On some inequalities for the gamma and psi functions Math. Comput. 66 373-389
  • [2] Alzer H.(2000)Inequalities for the volume of the unit ball in J. Math. Anal. Appl. 252 353-363
  • [3] Alzer H.(2008)Inequalities for the volume of the unit ball in Mediterr. J. Math. 5 395-413
  • [4] Anderson G.D.(1997)A monotoneity property of the gamma function Proc. Am. Math. Soc. 125 3355-3362
  • [5] Qiu S.-L.(1989)Special functions of quasiconformal theory Expo. Math. 7 97-136
  • [6] Anderson G.D.(1997)A continuous analogue of Sperner’s theorem Commun. Pure Appl. Math. 50 205-223
  • [7] Vamanamurthy M.K.(2009)An ultimate extremely accurate formula for approximation of the factorial function Arch. Math. (Basel) 93 37-45
  • [8] Vuorinen M.(2010)New approximations of the gamma function in terms of the digamma function Appl. Math. Lett. 23 97-100
  • [9] Klain D.A.(2009)Complete monotonic functions associated with gamma function and applications Carpathian J. Math. 25 186-191
  • [10] Rota G.-C.(2010)Best estimates of the generalized Stirling formula Appl. Math. Comput. 215 4044-4048