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Supplements to a class of logarithmically completely monotonic functions associated with the gamma function. (English) Zbl 1139.33300
Summary: The authors present a necessary condition, a sufficient condition and a necessary and sufficient condition for a class of functions associated with the gamma function to be logarithmically completely monotonic. As a consequence of these results, supplements to the recent investigation by S.-L. Qiu and M. Vuorinen [Math. Comput. 74, No. 250, 723–742 (2005; Zbl 1060.33006)] are provided and a new Kečkić-Vasić type inequality is concluded.

33B15 Gamma, beta and polygamma functions
26D05 Inequalities for trigonometric functions and polynomials
Full Text: DOI
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