تقرير
Some Representations of the Deformed Euler Numbers ${\rm e}_{s,t,u}$ and Proof for Irrationality
| العنوان: | Some Representations of the Deformed Euler Numbers ${\rm e}_{s,t,u}$ and Proof for Irrationality |
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| المؤلفون: | López, Ronald Orozco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Primary 11J72. Secondary 11A67, 11J70, 11B39, 33E20 |
| الوصف: | In this paper, representations of the Euler $(s,t)$-numbers ${\rm e}_{s,t,u}$ are given: as series compression, as Engel series expansion, as a series of partial Theta functions, as a continued fraction and as the limit of a sequence. Furthermore, it is proved 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 $\vert au\vert>1$. This is the first step in a program to study the irrationality of $(s,t)$-analog of known numbers. Comment: 24 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.15930 |
| رقم الأكسشن: | edsarx.2406.15930 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |