Inequalities for the Lugo and Euler–Mascheroni constants

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