Increasing property and logarithmic convexity concerning Dirichlet beta function, Euler numbers, and their ratios

被引：3
|
作者：
Qi, Feng [1 ]
Yao, Yong -Hong [2 ]
机构：
[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Peoples R China
[2] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2023年 / 52卷 / 01期
关键词：
Dirichlet beta function; Euler number; increasing property; logarithmic convexity; ratio; integral representation;
D O I：
10.15672/hujms.1099250
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, by virtue of an integral representation of the Dirichlet beta function, with the aid of a relation between the Dirichlet beta function and the Euler numbers, and by means of a monotonicity rule for the ratio of two definite integrals with a parameter, the author finds increasing property and logarithmic convexity of two functions and two sequences involving the Dirichlet beta function, the Euler numbers, and their ratios.
引用
收藏
页码：17 / 22
页数：6
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