DLMF:26.8.E35 (Q7863)

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DLMF:26.8.E35
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    Statements

    Defining formula
    ∑ j = 0 n j k = ∑ j = 0 k j ! ⁢ S ⁡ ( k , j ) ⁢ ( n + 1 j + 1 ) , superscript subscript 𝑗 0 𝑛 superscript 𝑗 𝑘 superscript subscript 𝑗 0 𝑘 𝑗 Stirling-number-second-kind-S 𝑘 𝑗 binomial 𝑛 1 𝑗 1 {\displaystyle{\displaystyle\sum_{j=0}^{n}j^{k}=\sum_{j=0}^{k}j!S\left(k,j% \right)\genfrac{(}{)}{0.0pt}{}{n+1}{j+1},}}
    0 references
    DLMF id
    DLMF:26.8.E35
    0 references
    Symbols used
    Q12131
    Defining formula
    S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p3.m2ardec
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