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arXiv · 2405.12246

A Family of New Formulas for the Euler-Mascheroni Constant

Noah Ripke
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Abstract

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.

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Noah Ripke. 2024-05-18. A Family of New Formulas for the Euler-Mascheroni Constant. https://arxiv.org/abs/2405.12246

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