Pre Stieltjes Functions |
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Authors: | Henrik L. Pedersen |
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Affiliation: | 1. Department of Basic Sciences and Environment, Mathematics and Computer Science, Faculty of Life Sciences, University of Copenhagen, 40, Thorvaldsensvej, DK-1871, Frederiksberg C, Denmark
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Abstract: | In this paper we characterize the class Ck{{mathcal{C}_k}} of functions f on (0,∞) for which f(x), . . . ,(x k f(x))(k) are completely monotonic for given k. In the limit we obtain the well-known characterization of the class of Stieltjes functions as those functions f defined on the positive half line for which (x k f(x))(k) is completely monotonic on (0,∞) for all k ≥ 0. |
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