New representations for the Lugo and Euler–Mascheroni constants

Abstract

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