Logarithmically completely monotonic functions relating to the gamma function |
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| Authors: | Chao-Ping Chen Feng Qi |
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| Institution: | a College of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan 454010, China
b Research Institute of Mathematical Sciences, Henan Polytechnic University, Jiaozuo City, Henan 454010, China |
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| Abstract: | In this paper, the logarithmically complete monotonicity of the function exΓ(x+β)/xx+β−α in (0,∞) for α∈R and β?0 is considered and the corresponding result by G.D. Anderson, R.W. Barnard, K.C. Richards, M.K. Vamanamurthy and M. Vuorinen is generalized. As applications of these results, some inequalities between identric mean and ratio of two gamma functions by J.D. Ke?ki? and P.M. Vasi? are extended. |
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| Keywords: | Gamma function Logarithmically completely monotonic function Mean value Inequality |
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