%0 Journal Article
%T A note on an open problem
%A Miao-Qing An
%J Tamkang Journal of Mathematics
%D 2012
%I Tamkang University
%R 10.5556/j.tkjm.43.2012.281-287
%X The function $frac{Gamma(x+1)^{frac1x}}{(x+eta)^{alpha}}$ is logarithmically completely monotonic on $(0,infty)$ for $alphage1$ and $0leetale1$, and is logarithmically completely monotonic in $(-1,0)$ for $0<alphale frac{2eta}{1+2eta}$ and $eta>1$. This give an answer to an open problem proposed by Feng Qi.
%K Gamma function
%K $ psi $ function
%K polygamma function
%K complete monotonicity
%U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/1184