A Complete Monotonicity of the Gamma Function

The function 1/x ln Γ(x+1)−ln x+1 is strictly completely monotonic on (0,∞)

Logarithmically Completely Monotonic Ratios of Mean Values and an Application

In the article, some strictly Logarithmically completely monotonic ratios of mean values are presented

Monotonicity and Inequalities for Ratio of the Generalized Logarithmic Means

Let c > b > a > 0 be real numbers. Then the function f(r) = Lr(a,b)/Lr(a,c) is strictly decreasing on (−∞,∞), where Lr(a, b) denotes the generalized (extended) logarithmic mean of two positive numbers a and b

Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2)

Inequalities and asymptotic expansions related to the volume of the unit ball in Rⁿ

Let Ωn=πn/2/Γ(n2+1)(n∈N)Ωn=πn/2/Γ(n2+1)(n∈N) denote the volume of the unit ball in RnRn. In this paper, we present asymptotic expansions and inequalities related to ΩnΩn and the quantities:Ωn−1Ωn,ΩnΩn−1+Ωn+1andΩ1/nnΩ1/(n+1)n+1