Remarks on complete monotonicity of a function involving the Gamma function

In the note, the authors give several remarks on the paper in “Chen and Haigang Zhou On completely monotone of an arbitrary real parameter function involving the gamma function. Applied Mathematics and Computation, 2014, vol. 242, pp. 658–663; DOI: 10.1016/j.amc.2014.05.034.” By virtue of these, the authors point out several trivial extensions and generalizations and establish some new results on the complete monotonicity of a function involving the classical Euler gamma function.