Some completely monotonic functions of positive order

Koumandos, Stamatis; Lamprecht, Martin

doi:10.1090/S0025-5718-09-02313-8

Some completely monotonic functions of positive order
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by Stamatis Koumandos and Martin Lamprecht PDF

Math. Comp. 79 (2010), 1697-1707 Request permission

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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