Gautchi's ratio and the Volume of the unit ball in R^n

Details Gautchi's ratio and the Volume of the unit ball in R^n Gautchi's ratio and the Volume of the unit ball in R^n

2009-12-11

arxiv.org/abs/0912.2182v2

Mathematics

Classical Analysis and ODEs

Scientific paper

Let Omega(n) be the volume of the unit ball in R^n. 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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