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

Feng Qi; Yong-hong Yao

Article Details

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

Authors:

Feng Qi | Yong-hong Yao

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.17-22

Document Type:

Article

Publication Date:

2/2023

Document Language:

English

Document ID (Org No.):

2001283996

pISSN:

2651-477X

Keywords:

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.

 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.

 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.

 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.

Article Details

Authors: Feng Qi | Yong-hong Yao

Publisher: Hacettepe University

Main Topics: Mathematical Sciences

Journal: Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.17-22

Document Type: Article

Publication Date: 2/2023

Document Language: English

Document ID (Org No.): 2001283996

pISSN: 2651-477X

Issues

Authors:

Feng Qi | Yong-hong Yao

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 1, pp.17-22

Document Type:

Article

Publication Date:

2/2023

Document Language:

English

Document ID (Org No.):

2001283996

pISSN:

2651-477X