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

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 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 γγ in terms of the psi (or digamma) function ψ(z)ψ(z), gave the bounds for the difference L−LnL−Ln and presented a new sequence which was shown to converge to Lugo’s constant LL. In this following article, we establish several further (presumably new) analytical representations for the Euler–Mascheroni constant γγ in terms of the psi (or digamma) function ψ(z)ψ(z).