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On a relation between the Riemann zeta function and the Stirling numbers. (English) Zbl 1202.11042

Summary: Let \(\zeta (z)\) be the Riemann zeta function and \(s(k, n)\) the Stirling numbers of the first kind. Shen proved the identity \[ \zeta (n+1) = \sum^{\infty}_{k=n} \frac {s(k,n)}{k\dot k!}\qquad (1 \leq n \in \mathbb Z). \] We give a short proof by elementary methods

MSC:

11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11B73 Bell and Stirling numbers
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