DLMF:24.6.E1 (Q7465)

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DLMF:24.6.E1
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    Statements

    test
    B 2 ⁢ n = ∑ k = 2 2 ⁢ n + 1 ( - 1 ) k - 1 k ⁢ ( 2 ⁢ n + 1 k ) ⁢ ∑ j = 1 k - 1 j 2 ⁢ n , Bernoulli-number-B 2 𝑛 superscript subscript 𝑘 2 2 𝑛 1 superscript 1 𝑘 1 𝑘 binomial 2 𝑛 1 𝑘 superscript subscript 𝑗 1 𝑘 1 superscript 𝑗 2 𝑛 {\displaystyle{\displaystyle B_{2n}=\sum_{k=2}^{2n+1}\frac{(-1)^{k-1}}{k}{2n+1% \choose k}\sum_{j=1}^{k-1}j^{2n},}}
    0 references
    DLMF id
    DLMF:24.6.E1
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q12116
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1dec
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    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
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    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1dec
    0 references
     
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