A Generalized Recurrence for fully degenerate Bell polynomials
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_ | 1866908656714383360 |
|---|---|
| author | Kim, Taekyun Kim, Dae San |
| author_facet | Kim, Taekyun Kim, Dae San |
| contents | This paper addresses the unnatural appearance of the two-variable degenerate Fubini polynomials in a recently derived Spivey-type recurrence relation for the fully degenerate Bell polynomials. To solve this, we introduce a new family of polynomial which we also call the fully degenerate Bell polynomials, along with their two-variable counterparts. Our main contribution is the derivation of natural Spivey-type recurrence relations using operator methods. We extend these results to the r-counterparts, the fully degenerate r-Bell polynomials providing Dobinski-like, finite sum, operator expressions, and Spivey-type recurrence relations for all the new polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalized Recurrence for fully degenerate Bell polynomials Kim, Taekyun Kim, Dae San Combinatorics Classical Analysis and ODEs Number Theory 11B73, 11B83, 47N99 This paper addresses the unnatural appearance of the two-variable degenerate Fubini polynomials in a recently derived Spivey-type recurrence relation for the fully degenerate Bell polynomials. To solve this, we introduce a new family of polynomial which we also call the fully degenerate Bell polynomials, along with their two-variable counterparts. Our main contribution is the derivation of natural Spivey-type recurrence relations using operator methods. We extend these results to the r-counterparts, the fully degenerate r-Bell polynomials providing Dobinski-like, finite sum, operator expressions, and Spivey-type recurrence relations for all the new polynomials. |
| title | A Generalized Recurrence for fully degenerate Bell polynomials |
| topic | Combinatorics Classical Analysis and ODEs Number Theory 11B73, 11B83, 47N99 |
| url | https://arxiv.org/abs/2511.12433 |