New $q$-identities Via $q$-Derivative of Basic Hypergeometric Series with Respect to Parameters
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916633562316800 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | In this paper, we use the effect of the $q$-differential and deformed $q$-exponential operators on basic hypergeometric series to find new $q$-identities from the $q$-Gauss sum, the $q$-Chu-Vandermonde's sum, and Jackson's transformation formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20109 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New $q$-identities Via $q$-Derivative of Basic Hypergeometric Series with Respect to Parameters López, Ronald Orozco Combinatorics Primary 05A30. Secondary 33D15 In this paper, we use the effect of the $q$-differential and deformed $q$-exponential operators on basic hypergeometric series to find new $q$-identities from the $q$-Gauss sum, the $q$-Chu-Vandermonde's sum, and Jackson's transformation formula. |
| title | New $q$-identities Via $q$-Derivative of Basic Hypergeometric Series with Respect to Parameters |
| topic | Combinatorics Primary 05A30. Secondary 33D15 |
| url | https://arxiv.org/abs/2502.20109 |