The asymptotic behaviour of a sequence considered by I. J. Schoenberg (Q5929783)
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scientific article; zbMATH DE number 1586511
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The asymptotic behaviour of a sequence considered by I. J. Schoenberg |
scientific article; zbMATH DE number 1586511 |
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The asymptotic behaviour of a sequence considered by I. J. Schoenberg (English)
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17 January 2002
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\textit{I. J. Schoenberg} [Nieuw Arch. Wiskd., III Ser. 30, 116 (Problem 640) (1982)] showed that \(\lim_{n \to\infty} S_n={1\over e-1}\), where \(S_n=(n+1)^{-n} \sum^n_{k=1} k^n\), \(n=1,2,\dots\). In this note the authors give complete asymptotic expansions of this sequence. They obtain several asymptotic expansions also in terms of special numbers. Modified sequence \(n^{-n}\sum^n_{k=1} k^n\) is also examined.
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asymptotic expansions
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Stirling numbers
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Touchard polynomials
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sequences
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