Inequalities 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≔{1,2,3,…}) as n→∞n→∞, where γγ denotes the Euler–Mascheroni constant. In this work, we establish new inequalities for the Lugo and Euler–Mascheroni constants.