论文标题
从涉及指数函数和总和到伽马函数比率的对数的单调性的不平等到对数的单调性
From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions
论文作者
论文摘要
在本文中，作者回顾了一系列不平等的起源，动机和概括，涉及多个指数功能和总和，建立了三个涉及有限的指数功能和总和的新不平等，通过找到与伯诺利数字的生成功能相关的函数的启用性，调查历史，一般性，否定性概述，概述了概述，概述了一般性的概念，并且均已完成。功能，当前的有限Trigamma功能的线性组合，构建有限γ功能的新比例，得出单调性，对数的凸度，凹度，完全单调性，以及两种有限胶功能的限制量的新构建比率，并提出了两种限制的限制量，构建了有限伽玛功能的新比例，构建了单调性，对数凸性，凹度，完全单调性和伯恩斯坦功能的特性。要研究的功能。
In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers, survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finite gamma functions, present complete monotonicity of a linear combination of finite trigamma functions, construct a new ratio of finite gamma functions, derives monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finite gamma functions, and suggest two linear combinations of finite trigamma functions and two ratios of finite gamma functions to be investigated.
