On Generalized Stieltjes Functions

Stamatis Koumandos, Henrik L. Pedersen*

*Corresponding author for this work

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Abstract

It is shown that a function f is a generalized Stieltjes function of order (Formula presented.) if and only if (Formula presented.) is completely monotonic for all (Formula presented.), thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions f for which (Formula presented.) is completely monotonic for all (Formula presented.) is obtained in terms of properties of the representing measure of f.

Original languageEnglish
JournalConstructive Approximation
Volume50
Issue number1
Pages (from-to)129-144
ISSN0176-4276
DOIs
Publication statusPublished - 2019

Keywords

  • Completely monotonic function
  • Generalized Stieltjes function
  • Laplace transform

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