On the computation of the Euler constant \({\gamma}\)
Let \(H(n)=n^2 \Bigl[1+{1 \over 2}+ \cdots+ {1\over n}-\log \Bigl( n+ {1\over 2}\Bigr) -C\Bigr],\) where \(C\) is the Euler constant. The author proves a conjecture of Matti Vuorinen which states that \(H(n)\) increases monotonically from \(H(1)=0.0173 \dots\) to \(\lim_{n\to \infty} H(n)=1/24= 0.0416 \dots\) \((n=1,2,3, \dots)\). There appear also some new formulas for the computation of \(C\).
scientific article; zbMATH DE number 1534765