Two monotonic functions involving gamma function and volume of unit ball

Abstract

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma (x)$ and relating to the $n$-dimensional volume of the unit ball ${\mathbb{B}}^n$ in ${\mathbb{R}}^n$.

7 pages

References in corpus (2)

• Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions
• An extension of an inequality for ratios of gamma functions

Cited by in corpus (2)

• Bounds for the ratio of two gamma functions--From Wendel's limit to Elezović-Giordano-Pečarić's theorem
• A logarithmically completely monotonic function involving the ratio of gamma functions