A completely monotonic function used in an inequality of Alzer

Details A completely monotonic function used in an inequality of Alzer A completely monotonic function used in an inequality of Alzer

2011-05-31

arxiv.org/abs/1105.6181v1

Mathematics

Classical Analysis and ODEs

13 pages

Scientific paper

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.

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