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Completely Monotone Functions: A Digest

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Analytic Number Theory, Approximation Theory, and Special Functions

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.

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Acknowledgement

This work is supported by Ministry of Education and Science of Serbia under projects 174024 and III 44006.

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Authors and Affiliations

  1. University of Belgrade, 35-54, 11000, Belgrade, Serbia

    Milan Merkle

  2. Union University, Računarski fakultet, Kneza Mihaila 6, 11000, Belgrade, Serbia

    Milan Merkle

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  1. Milan Merkle
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Correspondence to Milan Merkle .

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Editors and Affiliations

  1. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Gradimir V. Milovanović

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

Additional information

Dedicated to Professor Hari M. Srivastava

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Merkle, M. (2014). Completely Monotone Functions: A Digest. In: Milovanović, G., Rassias, M. (eds) Analytic Number Theory, Approximation Theory, and Special Functions. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0258-3_12

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