DLMF:26.8.E8 (Q7833): Difference between revisions

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Property / constraint
 

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

|x|<1
Property / constraint: | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}} / rank
 
Normal rank

Revision as of 17:20, 30 December 2019

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DLMF:26.8.E8
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    Statements

    n = 0 s ( n , k ) x n n ! = ( ln ( 1 + x ) ) k k ! , superscript subscript 𝑛 0 Stirling-number-first-kind-S 𝑛 𝑘 superscript 𝑥 𝑛 𝑛 superscript 1 𝑥 𝑘 𝑘 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}s\left(n,k\right)\frac{x^{n}}{n% !}=\frac{(\ln\left(1+x\right))^{k}}{k!},}}
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    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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