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

页码：17 / 22

页数：6

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