Approximations to Euler's constant

Kh. Hessami Pilehrood, T. Hessami Pilehrood

We study a problem of finding good approximations to Euler's constant $\gamma ={\lim }_{n\to \infty }{S}_n,$ where $S_n={\sum }_{k=1}^n\frac{1}{n}-\log (n+1),$ by linear forms in logarithms and har…