Gautchi's ratio and the Volume of the unit ball in Rn
Abstract
Let Omega(n) be the volume of the unit ball in Rn. We formulate as an infinite product the gamma function ratio gamma(x+1/2)/gamma(x),x>0, which allows us to reproduce and /or produce a variety of formulas and inequalities, some of them seemingly new, concerning Omega(n-1)/Omega(n),and (Omega(n))2/Omega(n-1)Omega(n+1)
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