A Note on the Rogers-Szegö Polynomial $q$-Differential Operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913571816865792 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | In this paper, we introduce the Rogers-Szegö deformed $q$-differential operators g$_{n}(bD_{q}|u)$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators g$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The deformed homogeneous Al-Salam-Carlitz polynomials $Ψ_{m}^{(q^{-n})}(ub,x|uq^{-1})$ can easily be represented by using the operators g$_{n}(bD_{q}|u)$. Identities relating the new general Al-Salam-Carlitz polynomial, defined by Cao et al., the generalized, and homogeneous Al-Salam-Carlitz polynomials $Φ_{m}^{(q^n)}(b,x|q)$ and basic hypergeometric series are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on the Rogers-Szegö Polynomial $q$-Differential Operators López, Ronald Orozco Combinatorics 05A30, 33D45, 33D15 In this paper, we introduce the Rogers-Szegö deformed $q$-differential operators g$_{n}(bD_{q}|u)$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators g$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The deformed homogeneous Al-Salam-Carlitz polynomials $Ψ_{m}^{(q^{-n})}(ub,x|uq^{-1})$ can easily be represented by using the operators g$_{n}(bD_{q}|u)$. Identities relating the new general Al-Salam-Carlitz polynomial, defined by Cao et al., the generalized, and homogeneous Al-Salam-Carlitz polynomials $Φ_{m}^{(q^n)}(b,x|q)$ and basic hypergeometric series are given. |
| title | A Note on the Rogers-Szegö Polynomial $q$-Differential Operators |
| topic | Combinatorics 05A30, 33D45, 33D15 |
| url | https://arxiv.org/abs/2411.02680 |