DLMF:24.14.E5 (Q7550)

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DLMF:24.14.E5
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    Statements

    Defining formula
    ∑ k = 0 n ( n k ) ⁢ E k ⁡ ( h ) ⁢ B n - k ⁡ ( x ) = 2 n ⁢ B n ⁡ ( 1 2 ⁢ ( x + h ) ) , superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Euler-polynomial-E 𝑘 ℎ Bernoulli-polynomial-B 𝑛 𝑘 𝑥 superscript 2 𝑛 Bernoulli-polynomial-B 𝑛 1 2 𝑥 ℎ {\displaystyle{\displaystyle\sum_{k=0}^{n}{n\choose k}E_{k}\left(h\right)B_{n-% k}\left(x\right)=2^{n}B_{n}\left(\tfrac{1}{2}(x+h)\right),}}
    0 references
    DLMF id
    DLMF:24.14.E5
    0 references
    Symbols used
    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2aadec
    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.m2abdec
    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.m1ddec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1ddec
    0 references
     
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