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DLMF:26.8.E9

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Formula:8527
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MaRDI QIDQ8527

  • Label: DLMF:26.8.E9


Digital Library of Mathematical Functions ID 26.8.E9

∑ n , k = 0 ∞ s ⁡ ( n , k ) ⁢ x n n ! ⁢ y k = ( 1 + x ) y , superscript subscript 𝑛 𝑘 0 Stirling-number-first-kind-S 𝑛 𝑘 superscript 𝑥 𝑛 𝑛 superscript 𝑦 𝑘 superscript 1 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{n,k=0}^{\infty}s\left(n,k\right)\frac{x^{n}}% {n!}y^{k}=(1+x)^{y},}}


Constraint(s)

| x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}

Symbols List

  • s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}} :
  • ! {\displaystyle{\displaystyle!}} :
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  •  Edit this on Wikidata

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