Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.14324 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908662226747392 |
|---|---|
| author | Zacharovas, Vytas |
| author_facet | Zacharovas, Vytas |
| contents | We investigate depoissonization, the problem of recovering asymptotics of sequence coefficients from their exponential generating function. Classical approaches rely on complex-analytic growth conditions, but here we develop real-variable methods that avoid such assumptions. We also address the inverse problem, deriving asymptotic expansions of the generating function itself in terms of its coefficients, thereby extending Ramanujan's original expansion. Taken together, these results offer a unified and elementary framework for depoissonization and its reverse, with applications to analytic combinatorics and probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Elementary Approach to Depoissonization Zacharovas, Vytas Combinatorics Classical Analysis and ODEs 41A60 We investigate depoissonization, the problem of recovering asymptotics of sequence coefficients from their exponential generating function. Classical approaches rely on complex-analytic growth conditions, but here we develop real-variable methods that avoid such assumptions. We also address the inverse problem, deriving asymptotic expansions of the generating function itself in terms of its coefficients, thereby extending Ramanujan's original expansion. Taken together, these results offer a unified and elementary framework for depoissonization and its reverse, with applications to analytic combinatorics and probability. |
| title | An Elementary Approach to Depoissonization |
| topic | Combinatorics Classical Analysis and ODEs 41A60 |
| url | https://arxiv.org/abs/2511.14324 |