A note on a curious formula for Euler's constant

TL;DR

This paper uses the residue theorem to derive a generalized formula for Euler's constant, expanding on an existing infinite series by Flajolet, Gourdon, and Dumas.

Contribution

It introduces a generalized infinite series formula for Euler's constant using complex analysis techniques, specifically the residue theorem.

Findings

Derived a new generalized series for Euler's constant

Extended previous work by Flajolet, Gourdon, and Dumas

Demonstrated the application of residue theorem in constant formulas

Abstract

In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.