%0 Journal Article
%T A completely monotonic function used in an inequality of Alzer
%A Christian Berg
%A Henrik L. Pedersen
%J Mathematics
%D 2011
%I arXiv
%X The function $G(x)=(1-\ln x /\ln(1+x))x\ln x$ has been considered by Alzer, Qi and Guo. We prove that $G'$ is completely monotonic by finding an integral representation of the holomorphic extension of $G$ to the cut plane. A main difficulty is caused by the fact that $G'$ is not a Stieltjes function.
%U http://arxiv.org/abs/1105.6181v1