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 language | English |
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Journal | Constructive Approximation |
Volume | 50 |
Issue number | 1 |
Pages (from-to) | 129-144 |
ISSN | 0176-4276 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Completely monotonic function
- Generalized Stieltjes function
- Laplace transform