Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions

被引：7
作者：
Qi, Feng [1 ,2 ]
机构：
[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
[2] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 02期
关键词：
Bernoulli number; ratio; generating function; complete monotonicity; gamma function; digamma function; trigamma function; logarithmic derivative; linear combination; inequality; INTEGRAL-REPRESENTATIONS; LIMIT FORMULAS; INEQUALITIES; BOUNDS; PROOFS;
D O I：
10.1007/s10473-022-0206-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finitely many gamma functions, finds complete monotonicity of the second logarithmic derivative of the ratio, and simply reviews the complete monotonicity of several linear combinations of finitely many digamma or trigamma functions.
引用
收藏
页码：511 / 520
页数：10
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