A $q$-Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912745630203904 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | We use a new $q$-exponential operator based on the $q^{\pm1}$-derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}ψ_{1}$, ${}_{1}ψ_{1}$, ${}_{1}ψ_{2}$, and ${}_{2}ψ_{2}$. In addition, we provide summation formulas for bilateral series whose terms are basic hypergeometric functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $q$-Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series López, Ronald Orozco Combinatorics Primary 33E15. Secondary 11F27 We use a new $q$-exponential operator based on the $q^{\pm1}$-derivative $\D_{q^{\pm1}}$ of order 1 to derive summation formulas for bilateral basic hypergeometric series ${}_{0}ψ_{1}$, ${}_{1}ψ_{1}$, ${}_{1}ψ_{2}$, and ${}_{2}ψ_{2}$. In addition, we provide summation formulas for bilateral series whose terms are basic hypergeometric functions. |
| title | A $q$-Exponential Operator Based on the Derivative of Order 1 and Summation of Bilateral Basic Hypergeometric Series |
| topic | Combinatorics Primary 33E15. Secondary 11F27 |
| url | https://arxiv.org/abs/2512.03084 |