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

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Abstract

For the horizontal generating functions Pn(z)=∑nk=1 S(nk) 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.

Keywords

Stirling numbers of the second kind
generating functions
asymptotic zero distribution

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Communicated by Doron, S. Lubinsky

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E-mail: [email protected]