Stirling Numbers and Inverse Factorial Series

We study inverse factorial series and their relation to Stirling numbers of the first kind.We prove a special representation of the polylogarithm function in terms of series with such numbers.Using various identities for Stirling numbers of the first kind we construct a number of expansions of functions in terms of inverse factorial series where the coefficients are special numbers.These results are used to prove/reprove the asymptotic expansion of some classical functions.We also prove a binomial formula involving inverse factorials.