Newton series representation of completely monotone functions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917008909533184 |
|---|---|
| author | Lamby, Thomas Marichal, Jean-Luc Zenaïdi, Naïm |
| author_facet | Lamby, Thomas Marichal, Jean-Luc Zenaïdi, Naïm |
| contents | We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be viewed as an analog of Bernstein's little theorem for absolutely monotone functions. As an application, we use it to study principal indefinite sums, which are constructed via a broad generalization of Bohr-Mollerup's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newton series representation of completely monotone functions Lamby, Thomas Marichal, Jean-Luc Zenaïdi, Naïm Classical Analysis and ODEs Discrete Mathematics Combinatorics 26A48, 26A51, 39A70, 41A58 (Primary), 33B15, 39A12, 40A30 (Secondary) We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be viewed as an analog of Bernstein's little theorem for absolutely monotone functions. As an application, we use it to study principal indefinite sums, which are constructed via a broad generalization of Bohr-Mollerup's theorem. |
| title | Newton series representation of completely monotone functions |
| topic | Classical Analysis and ODEs Discrete Mathematics Combinatorics 26A48, 26A51, 39A70, 41A58 (Primary), 33B15, 39A12, 40A30 (Secondary) |
| url | https://arxiv.org/abs/2510.11577 |