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 |
|---|---|
| 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