DLMF:24.4.E14 (Q7427)

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DLMF:24.4.E14
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    Statements

    Defining formula
    E n - 1 ⁡ ( x ) = 2 n ⁢ ∑ k = 0 n ( n k ) ⁢ ( 1 - 2 k ) ⁢ B k ⁢ x n - k , Euler-polynomial-E 𝑛 1 𝑥 2 𝑛 superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 1 superscript 2 𝑘 Bernoulli-number-B 𝑘 superscript 𝑥 𝑛 𝑘 {\displaystyle{\displaystyle E_{n-1}\left(x\right)=\frac{2}{n}\sum_{k=0}^{n}{n% \choose k}(1-2^{k})B_{k}x^{n-k},}}
    0 references
    DLMF id
    DLMF:24.4.E14
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2afdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1gdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1mdec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1hdec
    0 references
     
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