A note on the denominators of Bernoulli numbers (Q464682)
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scientific article; zbMATH DE number 6362127
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the denominators of Bernoulli numbers |
scientific article; zbMATH DE number 6362127 |
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A note on the denominators of Bernoulli numbers (English)
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29 October 2014
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Bernoulli numbers
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Stirling numbers
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Using the von Staudt-Clausen theorem the authors prove an interesting formula for the denominator of the Bernoulli numbers \(B_m\) involving the Stirling numbers of the second kind \(S(k,n)\).NEWLINENEWLINEPut \(\tilde S(k,n)=k!S(k,n)\) then the formula NEWLINE\[NEWLINE\gcd(\tilde S(2n+1,2), \ldots, \tilde S(2n+1,2n+1)) = \text{denominator of}\;B_{2n}NEWLINE\]NEWLINE holds.
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