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

Authors : Feng Qİ, Yong-hong YAO

Pages : 17-22

Doi:10.15672/hujms.1099250

View : 16 | Download : 5

Publication Date : 2023-02-15

Article Type : Research Paper

Abstract :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.
Keywords : Dirichlet beta function, Euler number, increasing property, logarithmic convexity, ratio, integral representation