A SOLUTION TO QI’S EIGHTH OPEN PROBLEM ON COMPLETE MONOTONICITY

Abstract

n this paper, the complete monotonicity of 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