A formula connecting the Bernoulli numbers with the Stieltjes constants

TL;DR

This paper demonstrates that a recent formula connecting Bernoulli numbers to Stieltjes constants is mathematically equivalent to an earlier known representation, clarifying their relationship.

Contribution

It establishes the equivalence between a recent and an earlier formula relating Bernoulli numbers and Stieltjes constants.

Findings

The recent formula by Coffey is equivalent to Briggs and Chowla's earlier representation.

Clarifies the mathematical relationship between Bernoulli numbers and Stieltjes constants.

Provides insight into the historical development of formulas involving these constants.

Abstract

We show that the formula recently derived by Coffey for the Stieltjes constants in terms of the Bernoulli numbers is mathematically equivalent to the much earlier representation derived by Briggs and Chowla.