Geodesic
Logarithmically complete monotonicity of reciprocal ARCTAN function
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 1, p. 105

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We prove the conjecture stated in F. Qi and R. Agarwal, \emph{On complete monotonicity for several classes of functions related to ratios of gamma functions}, J. Inequal. Appl. (2019), that the function $1/\arctan$ is logarithmically completely monotonic on $(0,\infty)$, but not a Stieltjes transform.
Classification : 26A48, 30E20
Keywords: complete monotonicity, Stieltjes transform 
Vladimir Jovanović; Milanka Treml. Logarithmically complete monotonicity of reciprocal ARCTAN function. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 1, p. 105 . http://geodesic.mathdoc.fr/item/KJM_2025_49_1_a8/
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     title = {Logarithmically complete monotonicity of reciprocal {ARCTAN} function},
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