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Formula:8560

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Digital Library of Mathematical Functions ID 26.8.E39

∑ 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}.}}


Constraint(s)

Symbols List

  • δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}} :
  • s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}} :
  • S ⁡ ( n , k ) Stirling-number-second-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle S\left(\NVar{n},\NVar{k}\right)}} :
  • j 𝑗 {\displaystyle{\displaystyle j}} : nonnegative integer
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
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