Complete monotonicity of a function involving the divided difference of digamma functions

被引：24

作者：

Qi Feng ^{[1
]}

Luo QiuMing ^{[2
]}

Guo BaiNi ^{[1
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454010, Peoples R China

[2] Chongqing Normal Univ, Dept Math, Chongqing 401331, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2013年 / 56卷 / 11期

关键词：

necessary and sufficient condition; completely monotonic function; logarithmically completely monotonic function; divided difference; psi function; inequality for sums; bound for the ratio of two gamma functions; GAMMA FUNCTIONS; POLYGAMMA FUNCTIONS; PROPERTY;

D O I：

10.1007/s11425-012-4562-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.

引用

页码：2315 / 2325

页数：11

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