Estimating the Apéry's constant (Q2917669)
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scientific article; zbMATH DE number 6088919
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimating the Apéry's constant |
scientific article; zbMATH DE number 6088919 |
Statements
1 October 2012
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Apéry's constant
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rate of convergence
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inequalities
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0.8176417
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0.80168366
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Estimating the Apéry's constant (English)
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Apéry's constant is \(\zeta(3)=\sum k^{-3}\). The author uses a new series representation \(\zeta(3)=1+\sum (k^3+4k^7)^{-1}\) whose partial sums converge much more rapidly to \(\zeta(3)\) than those of \(\sum k^{-3}\).
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