DLMF:24.4.E15 (Q7428)

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DLMF:24.4.E15
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    Statements

    Defining formula
    B 2 ⁢ n = 2 ⁢ n 2 2 ⁢ n ⁢ ( 2 2 ⁢ n - 1 ) ⁢ ∑ k = 0 n - 1 ( 2 ⁢ n - 1 2 ⁢ k ) ⁢ E 2 ⁢ k , Bernoulli-number-B 2 𝑛 2 𝑛 superscript 2 2 𝑛 superscript 2 2 𝑛 1 superscript subscript 𝑘 0 𝑛 1 binomial 2 𝑛 1 2 𝑘 Euler-number-E 2 𝑘 {\displaystyle{\displaystyle B_{2n}=\frac{2n}{2^{2n}(2^{2n}-1)}\sum_{k=0}^{n-1% }{2n-1\choose 2k}E_{2k},}}
    0 references
    DLMF id
    DLMF:24.4.E15
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1adec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1hdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1ndec
    0 references
     
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