DLMF:26.8.E8 (Q7833)

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DLMF:26.8.E8
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    Statements

    Defining formula
    ∑ 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!},}}
    0 references
    DLMF id
    DLMF:26.8.E8
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    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.m5aedec
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