Proofs for a monotonicity result of a function involving the psi and exponential functions

Abstract

In the note, two alternative proofs are provided for a monotonicity result that the function $ψ(x)+\ln\bigl(e^{1/x}-1\bigr)$ is strictly increasing on $(0,\infty)$, where $ψ(x)$ is the psi function.

5 pages