Irrationality of the Deformed Euler Numbers ${\rm e}_{s,t,u}$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911974786334720 |
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| author | López, Ronald Orozco |
| author_facet | López, Ronald Orozco |
| contents | In this paper, we define the deformed Euler $(s,t)$-numbers ${\rm e}_{s,t,u}$ Furthermore, we prove that ${\rm e}_{as,a^2t,u^{-1}}$ and ${\rm e}_{as,a^2t,u^{-1}}^{-1}$ are irrational numbers when $a,u\in\mathbb{Q}$ and $\vert au\vert>1$, thus providing a countable infinite family of irrational numbers. This is the first step in a program to study the irrationality of $(s,t)$-analog of known numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irrationality of the Deformed Euler Numbers ${\rm e}_{s,t,u}$ López, Ronald Orozco Number Theory Primary 11J72. Secondary 11B39, 33E20 In this paper, we define the deformed Euler $(s,t)$-numbers ${\rm e}_{s,t,u}$ Furthermore, we prove that ${\rm e}_{as,a^2t,u^{-1}}$ and ${\rm e}_{as,a^2t,u^{-1}}^{-1}$ are irrational numbers when $a,u\in\mathbb{Q}$ and $\vert au\vert>1$, thus providing a countable infinite family of irrational numbers. This is the first step in a program to study the irrationality of $(s,t)$-analog of known numbers. |
| title | Irrationality of the Deformed Euler Numbers ${\rm e}_{s,t,u}$ |
| topic | Number Theory Primary 11J72. Secondary 11B39, 33E20 |
| url | https://arxiv.org/abs/2406.15930 |