Inequalities for the Volume of the Unit Ball in Rn

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).