A complete monotonicity property of the gamma function
A real valued \(C^{\infty}\) function \(f\) is strictly completely monotonic on an interval \(I\) if \((-1)^k f^{(k)}(x)>0\) for all \(x\in I,\, k\in \mathbb{N}\). For the gamma function the result is offered that \(x\mapsto 1-\ln x+(\ln \Gamma(x+1))/x\) is strictly completely monotonic on \(]0,\infty[\) and its limits at \(0\) and \(\infty\) are \(\infty\) and \(0,\) respectively.
scientific article; zbMATH DE number 2092949