Some new quicker approximations of Glaisher–Kinkelin's and Bendersky–Adamchik's constants

In this paper, some new polynomial 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, some numerical computations are also given.