Inequalities for the Landau constant (Q2777496)
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scientific article; zbMATH DE number 1717362
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities for the Landau constant |
scientific article; zbMATH DE number 1717362 |
Statements
7 March 2002
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Landau constant
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digamma function
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Inequalities for the Landau constant (English)
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The authors prove an asymptotic expansion for the \(n\)th Landau constant NEWLINE\[NEWLINE G_n=\sum _{i=0}^n \frac 1{2^{4i}} \binom{2i}{i}. NEWLINE\]NEWLINE This leads to a sharp inequality NEWLINE\[NEWLINE 1.0663<G_n-\frac 1\pi \psi \left(n+\frac 5 4\right)<1.0724, NEWLINE\]NEWLINE where \(\psi(x)\) is the logarithmic derivative of the \(\Gamma \)-function.
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