On fast converging sequences for constants of Bendersky type: Stirling, Glaisher–Kinkelin, Bendersky–Adamchik and some others

We exhibit some arbitrarily high order converging sequences for Bendersky constants which improves and generalizes the results of [J. Number Theory 133 (2013) pp. 2465–2469]. Our results rely on the Euler-Maclaurin formula and where already known to Benderski (1933) in some extent, but it apparently remained little known since. We also explain how to accelerate the convergence of the classical converging sequences by means of Richardson extrapolation