A Family of New Formulas for the Euler-Mascheroni Constant
Noah Ripke

TL;DR
This paper introduces a new family of formulas for the Euler-Mascheroni constant using the E-Harmonic function, aiming to aid in understanding its properties and potential irrationality.
Contribution
It presents novel formulas and approximations for the Euler-Mascheroni constant derived from the newly defined E-Harmonic function.
Findings
Two new formulas for the Euler-Mascheroni constant
A family of formulas derived from the E-Harmonic function
Potential tools for investigating the constant's irrationality
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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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods in inverse problems · Iterative Methods for Nonlinear Equations
