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Complete monotonicity and related properties of some special functions


Authors: Stamatis Koumandos and Martin Lamprecht
Journal: Math. Comp. 82 (2013), 1097-1120
MSC (2010): Primary 33B15; Secondary 26D20, 26D15
DOI: https://doi.org/10.1090/S0025-5718-2012-02629-9
Published electronically: July 25, 2012
MathSciNet review: 3008851
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Abstract: We completely determine the set of $ s,t>0$ for which the function $ L_{s,t}(x):=x-\frac {\Gamma (x+t)}{\Gamma (x+s)}\,x^{s-t+1}$ is a Bernstein function, that is $ L_{s,t}(x)$ is positive with completely monotonic derivative on $ (0,\,\infty )$. The complete monotonicity of several closely related functions is also established.


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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/S0025-5718-2012-02629-9
Keywords: Gamma function, psi function, completely monotonic functions, Bernstein functions
Received by editor(s): February 28, 2011
Received by editor(s) in revised form: September 26, 2011
Published electronically: July 25, 2012
Additional Notes: The research for this paper was supported by the Leventis Foundation (Grant no. 3411-21041).
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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