Weak Asymptotics for the Generating Polynomials of the Stirling Numbers of the Second Kind Original Research Article

For the horizontal generating functions Pn(z)=∑nk=1 S(n, k) zk 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.