DLMF:24.6.E2 (Q7466)

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DLMF:24.6.E2
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    Statements

    Defining formula
    B n = 1 n + 1 ⁢ ∑ k = 1 n ∑ j = 1 k ( - 1 ) j ⁢ j n ⁢ ( n + 1 k - j ) / ( n k ) , Bernoulli-number-B 𝑛 1 𝑛 1 superscript subscript 𝑘 1 𝑛 superscript subscript 𝑗 1 𝑘 superscript 1 𝑗 superscript 𝑗 𝑛 binomial 𝑛 1 𝑘 𝑗 binomial 𝑛 𝑘 {\displaystyle{\displaystyle B_{n}=\frac{1}{n+1}\sum_{k=1}^{n}\sum_{j=1}^{k}(-% 1)^{j}j^{n}{\genfrac{(}{)}{0.0pt}{}{n+1}{k-j}}\Bigg{/}{\genfrac{(}{)}{0.0pt}{}% {n}{k}},}}
    0 references
    DLMF id
    DLMF:24.6.E2
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1adec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1adec
    0 references
     
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