p-ADIC STIRLING NUMBERS OF THE SECOND KIND

Let S(n,k) denote the Stirling numbers of the second kind. We prove that the p-adic limit of S(p(e)a+c, p(e)b+d) as e -> infinity exists for any integers a, b, c, and d with 0 < b <= a. We call the limiting p-adic integer S(p(infinity)a+c, p(infinity)b+d). When a b mod (p - 1) or d <= 0, we express them in terms of p-adic binomial coefficients ((p infinity alpha-1) (p infinity beta))introduced in a recent paper.