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On Lindelöf’s error bound for Stirling’s series. (English) Zbl 0684.30003

For \(\pi /4<\theta <\pi /2\), the smallest (n-independent) constant C(\(\theta)\) which can be chosen such that \[ | R_ n(z)| \leq A_ n/(r^{2n+1})\cdot C(\theta)\quad (z=re^{i\theta}) \] is valid for all \(r>0\) and \(n\in {\mathbb{N}}_ 0\) is \(C(\theta)=(\sin (2\theta))^{- 1}\).
Reviewer: F.W.Schäfke

MSC:

30B50 Dirichlet series, exponential series and other series in one complex variable
33B10 Exponential and trigonometric functions
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