Completely monotonic functions related to the gamma and the q-gamma functions

Abstract

In this paper, two classes of completely monotonic functions involving the gamma function are investigated and exploited to establish sharp inequalities for the gamma and the digamma functions. These results extend to the q-gamma function for all \(q>0\). Sharp bounds for the q-gamma and the q-digamma functions are provided in terms of the inverse hyperbolic function (arcsinh).