Several completely monotone functions related to DeTemple's sequence

Abstract

In this paper, we present the necessary and sufficient conditions such that several functions involving $R\left(x\right)=\psi \left(x+1/2\right)-\ln x$ with a parameter are completely monotone on $\left(0,\infty \right)$, where $\psi$ is the digamma function. This generalizes some known results and verifies a conjecture posed by Chen.

16 pages