Chao-Ping Chen

TL;DR: A logarithmically completely monotonic function is a function that is monotone on (0, ∞) on (1 − ln x+ 1 x + 1 x ln Γ(x+1) x /x is strictly monotony on ( 0,∞) as discussed by the authors.

TL;DR: The function [Γ(x + 1)](1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞) as mentioned in this paper.

TL;DR: In this paper, the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained by using the first Binet's formula and the best lower and upper bounds of the nth harmonic number are established.

TL;DR: In this article, the logarithmically complete monotonicity of the function e x Γ (x + β ) / x x + β − α in ( 0, ∞ ) for α ∈ R and β ⩾ 0 is considered and the corresponding result by G.D. Anderson, R.W. Barnard, K.C. Richards, M.K. Vamanamurthy and M.M. Vuorinen is generalized.

TL;DR: For all natural numbers n, let n!! denote a double factorial and then formula math. The constants 4 π - 1 and 1/4 are the best possible.