包含函数Γ（x）的对数完全单调函数及不等式

摘要

基于欧拉Gamma函数的奇特性质，利用函数的单调性理论以及一些简单函数的积分表达式与级数展开式证明了函数fα(x)，α∈R 和函数s(x)的对数完全单调性，并利用该性质得出了一个比原有结论更精确的不等式以及一个双边不等式。%Based on unique properties of the gamma function, this paper proves the logarithmically complete monotonicities of the function fα(x), α ∈ R and the function s(x) by the monotonicity theory, the integral representations and the series expansions of some simple functions. Using the property, it concludes a inequalities that is more accurate than the original conclusion and a two-side inequality.