Some new approximations of Glaisher–Kinkelin's and Bendersky–Adamchik's constants by continued fraction

In this paper, some new continued fraction approximations, inequalities and rates of convergence of Glaisher–Kinkelin's and Bendersky–Adamchik's constants are provided. Finally, for demonstrating the superiority of our new convergent sequences over the classical sequences and Mortici's sequences, some numerical computations are also given.