A completely monotonic function used in an inequality of Alzer
Berg, Christian · Pedersen, Henrik L.
Original · EN
The function G(x)=(1- x /(1+x))x 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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