Mathematics of Computation

Author(s): Stamatis Koumandos; Martin Lamprecht.
Journal: Math. Comp.
MSC (2010): Primary 33B15; Secondary 26D20, 26D15
Posted: November 9, 2009
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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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Retrieve articles in Mathematics of Computation with MSC (2010): 33B15, 26D20, 26D15

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: 10.1090/S0025-5718-09-02313-8
PII: S 0025-5718(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
Posted: 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.
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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