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.
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页码：2315 / 2325
页数：11
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