Weak asymptotics for the generating polynomials of the stirling numbers of the second kind

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