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Inequalities for the Landau constant. (English) Zbl 0984.11068
The authors prove an asymptotic expansion for the \(n\)th Landau constant \[ G_n=\sum _{i=0}^n \frac 1{2^{4i}} \binom{2i}{i}. \] This leads to a sharp inequality \[ 1.0663<G_n-\frac 1\pi \psi \left(n+\frac 5 4\right)<1.0724, \] where \(\psi(x)\) is the logarithmic derivative of the \(\Gamma \)-function.

11Y60 Evaluation of number-theoretic constants
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