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arXiv · 0912.2182

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

D. Karayannakis
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Abstract

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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D. Karayannakis. 2010-08-10. Gautchi's ratio and the Volume of the unit ball in R^n. https://arxiv.org/abs/0912.2182

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