DLMF:24.4.E17 (Q7430)

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DLMF:24.4.E17
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    Statements

    Defining formula
    E 2 ⁢ n = 1 - ∑ k = 1 n ( 2 ⁢ n 2 ⁢ k - 1 ) ⁢ 2 2 ⁢ k ⁢ ( 2 2 ⁢ k - 1 ) ⁢ B 2 ⁢ k 2 ⁢ k . Euler-number-E 2 𝑛 1 superscript subscript 𝑘 1 𝑛 binomial 2 𝑛 2 𝑘 1 superscript 2 2 𝑘 superscript 2 2 𝑘 1 Bernoulli-number-B 2 𝑘 2 𝑘 {\displaystyle{\displaystyle E_{2n}=1-\sum_{k=1}^{n}{2n\choose 2k-1}\frac{2^{2% k}(2^{2k}-1)B_{2k}}{2k}.}}
    0 references
    DLMF id
    DLMF:24.4.E17
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aedec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1abdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1afdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1jdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1pdec
    0 references
     
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