New representations for the Lugo and Euler–Mascheroni constants

Lugo’s constant LL given by L=−12−γ+ln2 is defined as the limit of the sequence (Ln)n∈N(Ln)n∈N defined by Ln:=∑i=1n∑j=1n1i+j−(2ln2)n+lnn(n∈N) as n→∞n→∞, NN being the set of positive integers. In this paper, we establish new analytical representations for the Euler–Mascheroni constant γγ in terms of the psi function. We also give the bounds of L−LnL−Ln and present a new sequence which converges to Lugo’s constant LL.