# Completely monotonic functions

@article{Miller2001CompletelyMF,
title={Completely monotonic functions},
author={K. S. Miller and Stefan G. Samko},
journal={Integral Transforms and Special Functions},
year={2001},
volume={12},
pages={389 - 402}
}
• Published 1 December 2001
• Mathematics
• Integral Transforms and Special Functions
In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function w is the Laplace transform of an infinitely divisible probability distribution on (0,∞), if and only if w = e-h , where the derivative of h is completely monotonic and h(0+) = 0.
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