On Mathieu's inequality (Q1381609)
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scientific article; zbMATH DE number 1130520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Mathieu's inequality |
scientific article; zbMATH DE number 1130520 |
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On Mathieu's inequality (English)
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3 January 1999
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The authors prove the following inequality: for all real numbers \(x\neq 0\) \[ {1\over x^2+1/(2\zeta(3))} < \sum_{n=1}^\infty {2n\over (n^2+x^2)^2} < {1\over x^2+1/6}. \] The authors also show that the constants \(1/(2\zeta(3))\) and \(1/6\) are best possible.
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Mathieu's inequality
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