| 一些特殊函数的完全单调性 |
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| 引用本文： | 元志芳,王连堂.一些特殊函数的完全单调性[J].纯粹数学与应用数学,2015(2):129-135. |
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| 作者姓名： | 元志芳 王连堂 |
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| 作者单位： | 西北大学数学学院,陕西 西安,710127 |
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| 摘 要： | 欧拉Gamma函数是一种非常重要的函数,在数学的许多分支以及物理、工程等学科中都有着十分重要的作用.而完全单调性以及对数完全单调性是Gamma函数的重要性质.主要证明了一些包含Gamma函数和Psi函数在内的特殊函数的完全单调性和对数完全单调性,并由此推出了一些重要的不等式.
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| 关 键 词： | 完全单调性 对数完全单调性 Gamma函数 Psi函数 充分必要条件 |
Complete monotonicity of some specific functions |
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| Yuan Zhifang,Wang Liantang.Complete monotonicity of some specific functions[J].Pure and Applied Mathematics,2015(2):129-135. |
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| Authors: | Yuan Zhifang Wang Liantang |
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| Institution: | Yuan Zhifang;Wang Liantang;College of Mathematics, Northwest University; |
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| Abstract: | The classical Euler gamma function is one of the most important special functions and has many extensive applications in many branches, for example, statistics, physics, engineering and so on. The complete monotonicity play a central role in studying the special functions. In this paper, some complete monotonicity and logarithmically complete monotonicity of some functions involving gamma functions is proved and some su?cient and necessary conditions for some special functions to be completely monotonic or logarithmically completely monotonic are proposed. |
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| Keywords: | complete monotonicity logarithmically completely monotonicity gamma function Psi function su?cient and necessary conditions |
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