DLMF:24.4.E12 (Q7425)

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DLMF:24.4.E12
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    Statements

    Defining formula
    B n ⁡ ( x + h ) = ∑ k = 0 n ( n k ) ⁢ B k ⁡ ( x ) ⁢ h n - k , Bernoulli-polynomial-B 𝑛 𝑥 ℎ superscript subscript 𝑘 0 𝑛 binomial 𝑛 𝑘 Bernoulli-polynomial-B 𝑘 𝑥 superscript ℎ 𝑛 𝑘 {\displaystyle{\displaystyle B_{n}\left(x+h\right)=\sum_{k=0}^{n}{n\choose k}B% _{k}\left(x\right)h^{n-k},}}
    0 references
    DLMF id
    DLMF:24.4.E12
    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.m2aedec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1edec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1kdec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1fdec
    0 references
     
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