Monotonicity and inequalities for the gamma function

被引：49
|
作者：
Yang, Zhen-Hang [1 ,2 ]
Tian, Jing-Feng [1 ]
机构：
[1] North China Elect Power Univ, Coll Sci & Technol, Ruixiang St 282, Baoding 071051, Peoples R China
[2] State Grid Zhejiang Elect Power Co, Res Inst, Dept Sci & Technol, Hangzhou 310014, Zhejiang, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
关键词：
gamma function; Laplace transform; complete monotonicity; inequality; ASYMPTOTIC FORMULAS; FACTORIAL FUNCTION; BURNSIDES FORMULA; SERIES; APPROXIMATION;
D O I：
10.1186/s13660-017-1591-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function x bar right arrow 1/24x(In Gamma(x + 1/2) - x In x + x - In root 2 pi) + 1 - 120/7 x(2) is strictly increasing from (0,infinity) onto (1, 1860/343). This not only yields some known and new inequalities for the gamma function, but also gives some completely monotonic functions related to the gamma function.
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收藏
页数：15
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