DLMF:24.6.E7 (Q7471)

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DLMF:24.6.E7
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    Statements

    Defining formula
    B n ⁡ ( x ) = ∑ k = 0 n 1 k + 1 ⁢ ∑ j = 0 k ( - 1 ) j ⁢ ( k j ) ⁢ ( x + j ) n , Bernoulli-polynomial-B 𝑛 𝑥 superscript subscript 𝑘 0 𝑛 1 𝑘 1 superscript subscript 𝑗 0 𝑘 superscript 1 𝑗 binomial 𝑘 𝑗 superscript 𝑥 𝑗 𝑛 {\displaystyle{\displaystyle B_{n}\left(x\right)=\sum_{k=0}^{n}\frac{1}{k+1}% \sum_{j=0}^{k}(-1)^{j}{k\choose j}(x+j)^{n},}}
    0 references
    DLMF id
    DLMF:24.6.E7
    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.m2adec
    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
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1fdec
    0 references
     
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