Some classes of completely monotonic functions, II

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Integral Representation of Some Functions Related to the Gamma Function (2004, background): “1 +s dµ(s) 2 ],[3],[5],[6],[8],[9].”
Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity (2007, background): “The functions of class L have been implicitly studied in [3], and Lemma 2.”
Inequalities for the gamma function (2008, background): “Recently numerous interesting inequalities for the gamma function have been proved by many mathematicians, we refer to [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 17, 20, 22], and the references therein.”
A PROPERTY OF LOGARITHMICALLY ABSOLUTELY MONOTONIC FUNCTIONS AND THE LOGARITHMICALLY COMPLETE MONOTONICITY OF A POWER-EXPONENTIAL FUNCTION (2009, background): “if and only if 0 < α ≤ 2β, which is a conclusion obtained in [4].”