A Family of New Formulas for the Euler-Mascheroni Constant
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910453712551936 |
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| author | Ripke, Noah |
| author_facet | Ripke, Noah |
| contents | We introduce and prove several new formulas for the Euler-Mascheroni Constant. This is done through the introduction of the defined E-Harmonic function, whose properties, in this paper, lead to two novel formulas, alongside a family of formulas. While the paper does introduce many new approximations, it does not exhaust the possibilities of the E-Harmonic function but provides a strong first dive into its natural conclusions. We hope that the diversity of new formulas may provide stepping stones to a proof (or disproof) of the irrationality of the Euler-Mascheroni constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Family of New Formulas for the Euler-Mascheroni Constant Ripke, Noah General Mathematics 40A05, 11B68 We introduce and prove several new formulas for the Euler-Mascheroni Constant. This is done through the introduction of the defined E-Harmonic function, whose properties, in this paper, lead to two novel formulas, alongside a family of formulas. While the paper does introduce many new approximations, it does not exhaust the possibilities of the E-Harmonic function but provides a strong first dive into its natural conclusions. We hope that the diversity of new formulas may provide stepping stones to a proof (or disproof) of the irrationality of the Euler-Mascheroni constant. |
| title | A Family of New Formulas for the Euler-Mascheroni Constant |
| topic | General Mathematics 40A05, 11B68 |
| url | https://arxiv.org/abs/2405.12246 |