On Generalized Stieltjes Functions

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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
Issue number1
Pages (from-to)129-144
Publication statusPublished - 2019

    Research areas

  • Completely monotonic function, Generalized Stieltjes function, Laplace transform

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ID: 203596168