Strong asymptotics of the generating polynomials of the Stirling numbers of the second kind (Q5933475)

Let \(Q_n(z) = \sum_{k=1}^n S(n,k) (nz)^k,\) where \(S(n,k)\) is the Stirling number of the second kind. The author proves an asymptotic formula for \(Q_n(z)\) with \(z \in {\mathbf C}\backslash[-e,0]\) and proves an Airy-asymptotic formula for \(Q_n\) as \(z \to -e\).