Double-sum Rogers-Ramanujan type identities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913098838835200 |
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| author | Chen, Duanyu Liu, Xiangxin Sun, Lisa Hui |
| author_facet | Chen, Duanyu Liu, Xiangxin Sun, Lisa Hui |
| contents | As the $q$-analog of Chebyshev polynomials, $q$-Hermite polynomials form a cornerstone in the family of $q$-orthogonal polynomials, which play a fundamental role in quantum algebra and mathematical physics. Recently, Andrews obtained a series of Rogers-Ramanujan type identities by constructing Bailey pairs from Chebyshev polynomials. In this paper, by applying the expansion formula of Chebyshev polynomials in terms of $q$-Hermite polynomials and using the orthogonality relations, we derive a series of Rogers-Ramanujan type identities on double sums, which further generalized the known results due to Andrews, Shi, Sun and Yao. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06248 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Double-sum Rogers-Ramanujan type identities Chen, Duanyu Liu, Xiangxin Sun, Lisa Hui Combinatorics 05A30, 33D45 As the $q$-analog of Chebyshev polynomials, $q$-Hermite polynomials form a cornerstone in the family of $q$-orthogonal polynomials, which play a fundamental role in quantum algebra and mathematical physics. Recently, Andrews obtained a series of Rogers-Ramanujan type identities by constructing Bailey pairs from Chebyshev polynomials. In this paper, by applying the expansion formula of Chebyshev polynomials in terms of $q$-Hermite polynomials and using the orthogonality relations, we derive a series of Rogers-Ramanujan type identities on double sums, which further generalized the known results due to Andrews, Shi, Sun and Yao. |
| title | Double-sum Rogers-Ramanujan type identities |
| topic | Combinatorics 05A30, 33D45 |
| url | https://arxiv.org/abs/2605.06248 |