DLMF:26.8.E24 (Q7852)

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DLMF:26.8.E24
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    Statements

    Defining formula
    S ⁡ ( n , k ) = ∑ j = k n S ⁡ ( j - 1 , k - 1 ) ⁢ k n - j , Stirling-number-second-kind-S 𝑛 𝑘 superscript subscript 𝑗 𝑘 𝑛 Stirling-number-second-kind-S 𝑗 1 𝑘 1 superscript 𝑘 𝑛 𝑗 {\displaystyle{\displaystyle S\left(n,k\right)=\sum_{j=k}^{n}S\left(j-1,k-1% \right)k^{n-j},}}
    0 references
    DLMF id
    DLMF:26.8.E24
    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.m2aldec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1edec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1sdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1xdec
    0 references
     
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