DLMF:26.8.E25 (Q7853)

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DLMF:26.8.E25
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    Statements

    Defining formula
    S ⁡ ( n + 1 , k + 1 ) = ∑ j = k n ( n j ) ⁢ S ⁡ ( j , k ) , Stirling-number-second-kind-S 𝑛 1 𝑘 1 superscript subscript 𝑗 𝑘 𝑛 binomial 𝑛 𝑗 Stirling-number-second-kind-S 𝑗 𝑘 {\displaystyle{\displaystyle S\left(n+1,k+1\right)=\sum_{j=k}^{n}\genfrac{(}{)% }{0.0pt}{}{n}{j}S\left(j,k\right),}}
    0 references
    DLMF id
    DLMF:26.8.E25
    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.m2amdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1addec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1fdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1tdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1ydec
    0 references
     
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