COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE DI- AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS

被引：35

作者：

Qi, Feng ^{[1
]}

Guo, Bai-Ni ^{[2
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang City 453007, Henan Province, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 06期

关键词：

Completely monotonic function; logarithmically completely monotonic function; monotonicity; convexity; divided difference; digamma function; trigamma function; ratio of two gamma functions; UNIT BALL; INEQUALITIES; BOUNDS; REFINEMENTS; EXTENSIONS; DIGAMMA; VOLUME; PROOF;

D O I：

10.3934/cpaa.2009.8.1975

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we establish the complete monotonicity of two functions involving divided differences of the digamma function psi and the trigamma function psi'. Applying these monotonicity, we provide an alternative proof for the monotonicity and convexity of a function derived from bounding the ratio of two gamma functions, procure the logarithmically completely monotonic property of a function involving the ratio of two gamma functions, and obtain new bounds for the ratio of two gamma functions.

引用

页码：1975 / 1989

页数：15

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