Investigations about the Euler–Mascheroni constant and harmonic numbers
Abstract We introduce a sequence of real functions which converges to the constant function x ↦ γ ${x\mapsto\gamma}$ where γ is the Euler–Mascheroni constant. We determine a point where the resulting approximation of γ is very fast. Furthermore, we use our approach to improve known estimates in the pursuit of a conjecture related to harmonic numbers, part of which is settled.