Some $q$-transformation formulas and Rogers-Ramanujan type identities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908414791122944 |
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| author | Xu, Chang Yang, Dunkun |
| author_facet | Xu, Chang Yang, Dunkun |
| contents | In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula with other $q$-series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain $75$ Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some $q$-transformation formulas and Rogers-Ramanujan type identities Xu, Chang Yang, Dunkun Combinatorics In this paper, we explore the role that Liu's transformation formula can play in discovering Rogers-Ramanujan type identities. Specifically, we combine Liu's transformation formula with other $q$-series summations to derive a series of parameterized identities. Thereafter, through careful selection of these parameters, we obtain $75$ Rogers-Ramanujan type identities from Slater's list, and uncover several new Rogers-Ramanujan type identities. |
| title | Some $q$-transformation formulas and Rogers-Ramanujan type identities |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.16711 |