A remark on the values of the Riemann zeta function (Q1343673)
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scientific article; zbMATH DE number 714599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on the values of the Riemann zeta function |
scientific article; zbMATH DE number 714599 |
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A remark on the values of the Riemann zeta function (English)
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29 January 1995
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Für reelle \(x\) und ganze \(a\geq 0\) sei \(S_ a(x)\) das eindeutig bestimmte Polynom in \(x\) vom Grad \(a+1\) mit rationalen Koeffizienten und \(S_ a(m)= \sum_{n=1}^{m-1} n^ a\) für alle natürlichen \(m\). Der Verf. gibt zwei Beweise für die Identität \[ \zeta(-a)= \int_ 0^ 1 S_ a(x)dx \qquad (a=0, 1,2, \dots) \] an.
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Riemann zeta function
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identity
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