DLMF:26.8.E9 (Q7834)

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DLMF:26.8.E9
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    Statements

    Defining formula
    ∑ 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},}}
    0 references
    DLMF id
    DLMF:26.8.E9
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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.m5afdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    Q12173
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1bdec
    0 references
    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1hdec
    0 references
     
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