Explicit upper bounds for the Stirling numbers of the first kind

We give explicit upper bounds for the Stirling numbers of first kind s(n,m) which are asymptotically sharp. The form such varies according to m lying in central or non-central regions {1,…,n}. In each case, we use a different probabilistic representation terms well known random variables show corresponding bounds. Some applications concerning Riemann zeta function and certain subset Comtet also provided.