  We discuss 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 Stirling 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 reprove the asymptotic expansion of
some classical functions. We also prove a binomial formula involving inverse
factorials.
