Two new Bailey pairs and their $q$-identities of Rogers-Ramanujan type modulo 15, 24, and 30
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914992733814784 |
|---|---|
| author | Xu, Jianan Ma, Xinrong |
| author_facet | Xu, Jianan Ma, Xinrong |
| contents | In this paper, we first establish two new Bailey pairs via finding two generalizations of Euler's pentagonal number theorem. Next, we specificize the Bailey lemmas with these two Bailey pairs. As applications, we finally establish some $q$-series transformations and $q$-identities of Rogers-Ramanujan type modulo 15, 24, and 30. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two new Bailey pairs and their $q$-identities of Rogers-Ramanujan type modulo 15, 24, and 30 Xu, Jianan Ma, Xinrong Combinatorics In this paper, we first establish two new Bailey pairs via finding two generalizations of Euler's pentagonal number theorem. Next, we specificize the Bailey lemmas with these two Bailey pairs. As applications, we finally establish some $q$-series transformations and $q$-identities of Rogers-Ramanujan type modulo 15, 24, and 30. |
| title | Two new Bailey pairs and their $q$-identities of Rogers-Ramanujan type modulo 15, 24, and 30 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.00680 |