Some geometric series for Euler's constant

TL;DR

This paper introduces rapidly converging geometric series representations of Euler's constant, analyzing the oscillatory behavior of their coefficients despite quadratic computational costs.

Contribution

It presents new series representations of Euler's constant with fast convergence and discusses the asymptotic oscillations of their coefficients.

Findings

Series converge geometrically fast

Coefficients exhibit asymptotic oscillations

Coefficients' computation has quadratic complexity

Abstract

We provide representations of Euler's constant $\gamma=0.577...$ as series which converge geometrically fast (but use coefficients whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are discussed.