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Completely Monotone Functions: A Digest

In: Analytic Number Theory, Approximation Theory, and Special Functions

Author

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  • Milan Merkle

    (University of Belgrade
    Union University, Računarski fakultet)

Abstract

This work has a purpose to collect selected facts about the completely monotone (CM) functions that can be found in books and papers devoted to different areas of mathematics. We opted for lesser known ones and for those which may help in determining whether or not a given function is completely monotone. In particular, we emphasize the role of representation of a CM function as the Laplace transform of a measure, and we present and discuss a little-known connection with log-convexity. Some of presented methods are illustrated by several examples involving Gamma and related functions.

Suggested Citation

  • Milan Merkle, 2014. "Completely Monotone Functions: A Digest," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 347-364, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_12
    DOI: 10.1007/978-1-4939-0258-3_12
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