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Asymptotic estimates of Stirling numbers. (English) Zbl 0784.11007
New asymptotic estimates are given for the Stirling numbers $S\left(m,n\right)$ of the first and second kind, as $n\to \infty$. The approximations are uniformly valid with respect to $m$. Many previous estimates have been valid only for certain ranges of $m$, e.g. when $n-m$ is small. The method used to obtain the estimates is based on a modification of the saddle method, described in the author’s earlier paper [Q. Appl. Math. 43, 103-123 (1985; Zbl 0581.33001)].

##### MSC:
 11B73 Bell and Stirling numbers