Journal
MEDITERRANEAN JOURNAL OF MATHEMATICS
Volume 11, Issue 2, Pages 299-314Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00009-013-0340-7
Keywords
Volume of the unit n-dimensional ball; gamma function; inequality
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The volume of the unit ball in R-n is defined by Omega(n) = pi(n/2)/Gamma(n/2+1), n - 1,2,3, ... , where Gamma denotes the classical gamma function of Euler. In several recently published papers numerous authors studied properties of Omega (n) . In particular, various inequalities involving Omega (n) are given in the literature. In this paper, we continue the work on this subject and offer new inequalities. More precisely, we offer sharp upper and lower bounds for Omega(2)(n)/Omega(n-1)Omega(n+1), Omega(n)/Omega(n-1)+Omega(n+1) and Omega(n).
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