一类函数的对数完全单调性

摘要

This article mainly studies the logarithmically completely monotonicity of the function Gλ,µ(x) and the function [Gλ,µ(x)]−1 by the discussion of the parameter λ, µ, using the monotonicity theory, the logarithmically completely monotonicity property of the existent function and the integral expressions. On the basis of this, we further get the necessary and sufficient conditions of the logarithmically completely monotonicity of the function Gλ,µ(x) and the function [Gλ,µ(x)]−1 under certain conditions.%通过对参数λ，µ的讨论，主要利用函数的单调性理论，已有对数完全单调函数的性质以及幂函数的积分表达式研究了函数Gλ，µ(x)及函数[Gλ，µ(x)]−1的对数完全单调性，并在此基础上得到了一定条件下函数Gλ，µ(x)及[Gλ，µ(x)]−1对数完全单调的充要条件。