DLMF:24.14.E4 (Q7549)

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DLMF:24.14.E4
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    Statements

    Defining formula
    ∑ k = 0 n ( n k ) ⁢ E k ⁢ E n - k = - 2 n + 1 ⁢ E n + 1 ⁡ ( 0 ) = - 2 n + 2 ⁢ ( 1 - 2 n + 2 ) ⁢ B n + 2 n + 2 . superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Euler-number-E 𝑘 Euler-number-E 𝑛 𝑘 superscript 2 𝑛 1 Euler-polynomial-E 𝑛 1 0 superscript 2 𝑛 2 1 superscript 2 𝑛 2 Bernoulli-number-B 𝑛 2 𝑛 2 {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}E_{k}E_{n-k}=-2^{n+1}E_{% n+1}\left(0\right)=-2^{n+2}(1-2^{n+2})\frac{B_{n+2}}{n+2}.}}
    0 references
    DLMF id
    DLMF:24.14.E4
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
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