DLMF:26.14.E11 (Q7962)

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DLMF:26.14.E11
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    Statements

    Defining formula
    B m = m 2 m ⁢ ( 2 m - 1 ) ⁢ ∑ k = 0 m - 2 ( - 1 ) k ⁢ ⟨ m - 1 k ⟩ , Bernoulli-number-B 𝑚 𝑚 superscript 2 𝑚 superscript 2 𝑚 1 superscript subscript 𝑘 0 𝑚 2 superscript 1 𝑘 Eulerian-number 𝑚 1 𝑘 {\displaystyle{\displaystyle B_{m}=\frac{m}{2^{m}(2^{m}-1)}\sum_{k=0}^{m-2}(-1% )^{k}\genfrac{<}{>}{0.0pt}{}{m-1}{k},}}
    0 references
    DLMF id
    DLMF:26.14.E11
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    constraint
    m ≥ 2 𝑚 2 {\displaystyle{\displaystyle m\geq 2}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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    Q12217
    Defining formula
    ⟨ n k ⟩ Eulerian-number 𝑛 𝑘 {\displaystyle{\displaystyle\genfrac{<}{>}{0.0pt}{}{\NVar{n}}{\NVar{k}}}}
    xml-id
    C26.S14.SS1.p3.m2ahdec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1idec
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    Q12171
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C26.S1.XMD5.m1dec
    0 references
     
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