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Asymptotic estimates of Stirling numbers. (English) Zbl 0784.11007
New asymptotic estimates are given for the Stirling numbers S(m,n) of the first and second kind, as n. 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:
11B73Bell and Stirling numbers