Weak Asymptotics for the Generating Polynomials of the Stirling Numbers of the Second Kind

For the horizontal generating functions Pn (z)= k=1 S(n, k) z k of the Stirling numbers of the second kind, a weak asymptotic is established, as n . The distribution function Fn of the zeros of Qn (z)=Pn (nz) is investigated and by using the Stieltjes transformation, the limit of Fn in the sense of weak convergence is deduced. 2001 Academic Press