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JOURNALS // Problemy Analiza — Issues of Analysis // Archive
Probl. Anal. Issues Anal., 2021 Volume 10(28), Issue 3, Pages 108–112 (Mi pa334)
A solution to Qi's eighth open problem on complete monotonicity

A. Venkata Lakshmi

Department of Mathematics, Osmania University, Hyderabad 500007, India

Abstract: In this paper, the complete monotonicity of $\frac{1}{\arctan x}$ is proved. This problem was posted by F. Qi and R. P. Agarwal as the eighth open problem of collection of eight open problems.

Keywords: logarithmically completely monotonic functions, polygamma function, inequalities, Stieltjes function.

UDC: 517.51, 517.58

MSC: 39B62, 33C10, 42A05

Received: 01.03.2021
Revised: 09.06.2021
Accepted: 11.06.2021

Language: English

DOI: 10.15393/j3.art.2021.10570



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© Steklov Math. Inst. of RAS, 2024