Asymptotic expansions for the stirling numbers of the first kind

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Asymptotic Expansions for the Stirling Numbers of the First Kind

Let s(n,m) denote the (unsigned) Stirling numbers of the first kind: s(n,m) := [w] (w(w + 1) · · · (w + n− 1)) (1 ≤ m ≤ n, n ≥ 1). Many different asymptotic expressions for s(n,m), as n→∞, have been proposed in the literature due to their wide applications, cf. Temme [8] for a brief survey of known results together with a uniform asymptotic expansion valid for all m, 1 ≤ m ≤ n. Recently, Wilf [...

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ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series A

سال: 1995

ISSN: 0097-3165

DOI: 10.1016/0097-3165(95)90010-1