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Some completely monotonic functions of positive order


Authors: Stamatis Koumandos and Martin Lamprecht
Journal: Math. Comp. 79 (2010), 1697-1707
MSC (2010): Primary 33B15; Secondary 26D20, 26D15
DOI: https://doi.org/10.1090/S0025-5718-09-02313-8
Published electronically: November 9, 2009
MathSciNet review: 2630008
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Abstract: We completely determine the set of $ (\alpha,\beta)\in\mathbb{R}^2$ for which the function $ \frac{e^{\alpha x} - e^{\beta x}}{e^x -1}$ is convex on $ (0,\infty)$ and use this result to give some special classes of completely monotonic functions of positive order related to gamma and psi functions.


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Additional Information

Stamatis Koumandos
Affiliation: Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus
Email: skoumand@ucy.ac.cy

Martin Lamprecht
Affiliation: Department of Mathematics and Statistics, The University of Cyprus, P. O. Box 20537, 1678 Nicosia, Cyprus
Email: martin@ucy.ac.cy

DOI: https://doi.org/10.1090/S0025-5718-09-02313-8
Keywords: Gamma function, psi function, completely monotonic functions
Received by editor(s): May 7, 2009
Received by editor(s) in revised form: June 16, 2009
Published electronically: November 9, 2009
Additional Notes: The research for this paper has been supported by the Leventis Foundation (Grant no. 3411-21041).
The authors would like to thank Setsuo Takato for his help with KETpic.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.