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

Year 2023, Volume: 52 Issue: 1, 17 - 22, 15.02.2023

Feng Qi , Yong-hong Yao

https://doi.org/10.15672/hujms.1099250

Cited By: 2

https://izlik.org/JA85LM44NS

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

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