Monotonicity and inequalities for the gamma function

被引：50

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.

引用

页数：15

共 37 条

[1] On some inequalities for the gamma and psi functions [J].