New representations for the Lugo and Euler–Mascheroni constants. II

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 an earlier investigation [C.-P. Chen, H.M. Srivastava, New representations for the Lugo and Euler–Mascheroni constants, Appl. Math. Lett. 24 (2011) 1239–1244] we established new analytical representations for the Euler–Mascheroni constant γ in terms of the psi (or digamma) function ψ ( z ) , gave the bounds for the difference L − L n and presented a new sequence which was shown to converge to Lugo’s constant L . In this following article, we establish several further (presumably new) analytical representations for the Euler–Mascheroni constant γ in terms of the psi (or digamma) function ψ ( z ) .