On the Heine Binomial Operators
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916449691369472 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | In this paper, we introduce the Heine binomial operators H$_{n}(bD_{q})$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators H$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The Hahn polynomials $Φ_{m}^{(q^n)}(b,x|q)$ can easily be represented by using the operators H$_{n}(bD_{q})$. Here, we derive $q$-exponential and ordinary generating function, Mehler's formula, Rogers formula, and other identities for the polynomials $Φ_{m}^{(q^n)}(b,x|q)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Heine Binomial Operators López, Ronald Orozco Combinatorics Primary 05A30. Secondary 33D45 In this paper, we introduce the Heine binomial operators H$_{n}(bD_{q})$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators H$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The Hahn polynomials $Φ_{m}^{(q^n)}(b,x|q)$ can easily be represented by using the operators H$_{n}(bD_{q})$. Here, we derive $q$-exponential and ordinary generating function, Mehler's formula, Rogers formula, and other identities for the polynomials $Φ_{m}^{(q^n)}(b,x|q)$. |
| title | On the Heine Binomial Operators |
| topic | Combinatorics Primary 05A30. Secondary 33D45 |
| url | https://arxiv.org/abs/2410.18058 |