Inequalities for the Volume of the Unit Ball in Rn, II

We present several sharp inequalities for the volume of the unit ball in R-n, W-n = pi(n/2)/Gamma(n/2+1), n is an element of N. One of our theorems states that the double-inequality A/root n <= (n+1) Omega n+1/Omega n - n Omega n/Omega/-1 < B/root n holds for all n >= 2 with the best possible constants A = (4-pi) root 2 = 1.2139... and B = 1/2 root 2 pi = 1.2533....