“…(1.12) Since then, many authors have made significant contributions to sharper the inequalities and the asymptotic expansions for G(n), see e.g. Alzer [2], Chen [9], Cvijović and Srivastava [13], Granath [22], Mortici [34], Nemes [36,37], Popa [38], Popa and Secelean [39], Zhao [46], Gavrea and M. Ivan [20], Chen and Choi [7,10,8], etc. To the best knowledge of the authors, the latest lower and upper bounds of G(n) along this research direction are due to Chen and Choi [8].…”