DLMF:26.8.E10 (Q7835)

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DLMF:26.8.E10
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    Statements

    Defining formula
    ∑ k = 1 n S ⁡ ( n , k ) ⁢ ( x - k + 1 ) k = x n , superscript subscript 𝑘 1 𝑛 Stirling-number-second-kind-S 𝑛 𝑘 subscript 𝑥 𝑘 1 𝑘 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\sum_{k=1}^{n}S\left(n,k\right)(x-k+1)_{k}=x^{n},}}
    0 references
    DLMF id
    DLMF:26.8.E10
    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.m2addec
    0 references
    Q12173
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1cdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1idec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1jdec
    0 references
     
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