The Decay constants of $B_c(nS)$ and $B_c^{\ast }(nS)$

The decay constants of the low lying S-wave $B_c$ mesons, i.e. $B_c(nS)$ and $B_c^{\ast }(nS)$ with $n\le 3$, are calculated in the nonrelativistic quark model. The running coupling of the strong interaction is taken into account, and the uncertainties due to varying parameters and losing Lorentz covariance are considered carefully. As a byproduct, the decay constants of the low lying S-wave charmonium and bottomium states are given in the appendixes.