DLMF:26.8.E39 (Q7867)

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DLMF:26.8.E39
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    Statements

    Defining formula
    ∑ j = k n s ⁡ ( j , k ) ⁢ S ⁡ ( n , j ) = ∑ j = k n s ⁡ ( n , j ) ⁢ S ⁡ ( j , k ) = δ n , k . superscript subscript 𝑗 𝑘 𝑛 Stirling-number-first-kind-S 𝑗 𝑘 Stirling-number-second-kind-S 𝑛 𝑗 superscript subscript 𝑗 𝑘 𝑛 Stirling-number-first-kind-S 𝑛 𝑗 Stirling-number-second-kind-S 𝑗 𝑘 Kronecker 𝑛 𝑘 {\displaystyle{\displaystyle\sum_{j=k}^{n}s\left(j,k\right)S\left(n,j\right)=% \sum_{j=k}^{n}s\left(n,j\right)S\left(j,k\right)=\delta_{n,k}.}}
    0 references
    DLMF id
    DLMF:26.8.E39
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5aadec
    0 references
    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5atdec
    0 references
    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.m2audec
    0 references
    Q12176
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C26.S1.XMD3.m1mdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1afdec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1akdec
    0 references
     
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