New sequence converging towards the Euler–Mascheroni constant

Let γ=0.577215664…γ=0.577215664… denote the Euler–Mascheroni constant, and let the sequence wn(a,b,c,d)=∑k=1n1k−ln(n+a+bn+cn2+dn3). The main aim of this paper is to determine the values a,b,c,da,b,c,d which provide the fastest sequence (wn)n≥1(wn)n≥1 approximating the Euler–Mascheroni constant.