Logarithmically complete monotonicity of reciprocal arctan function

Published 18 Dec 2021 in math.CA | (2112.09960v1)

Abstract: We prove the conjecture stated in F. Qi and R. Agarwal, \textit{On complete monotonicity for several classes of functions related to ratios of gamma functions}, J. Inequal. Appl. (2019), 1-42, that the function $1/\arctan$ is logarithmically completely monotonic on $(0,\infty)$, but not a Stieltjes transform.

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