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Formula:8258

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Digital Library of Mathematical Functions ID 24.15.E8

βˆ‘ k = 0 n ( - 1 ) n + k ⁒ s ⁑ ( n + 1 , k + 1 ) ⁒ B k = n ! n + 1 . superscript subscript π‘˜ 0 𝑛 superscript 1 𝑛 π‘˜ Stirling-number-first-kind-S 𝑛 1 π‘˜ 1 Bernoulli-number-B π‘˜ 𝑛 𝑛 1 {\displaystyle{\displaystyle\sum_{k=0}^{n}(-1)^{n+k}s\left(n+1,k+1\right)B_{k}% =\frac{n!}{n+1}.}}


Constraint(s)

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • s ⁑ ( n , k ) Stirling-number-first-kind-S 𝑛 π‘˜ {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}} :
  • ! {\displaystyle{\displaystyle!}} :
  • k π‘˜ {\displaystyle{\displaystyle k}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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