A New Identity for Euler's Constant via the Odd Harmonic Series with Dyadic Grouping - A Handwritten Manuscript

Abstract

This is a scanned copy of the handwritten manuscript. This manuscript presents several new mathematical formulas and identities for Euler's constant via the Odd Harmonic Series sum within Dyadic layers, which were independently derived by the author. Preliminary numerical experiments demonstrate convergence of the proposed representations to Euler’s constant, while the dyadic layer odd harmonic sums empirically exhibit O(4^{-k}) convergence toward (1/2)*ln2, indicating the potential for rapidly convergent representations and further analytical development. The uploaded file contains handwritten logical derivations and proofs. This work is made publicly available under the CC-BY 4.0 license, primarily intended for academic exchange and intellectual property archiving (timestamping). Peers and researchers are highly welcome to perform computational numerical verifications or theoretical extensions based on these results. For any future citations or derivative works, please properly cite the DOI of this Zenodo record.