DLMF:4.13.E5 (Q1646)

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DLMF:4.13.E5
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    Statements

    Defining formula
    Wp ⁡ ( x ) = ∑ n = 1 ∞ ( - 1 ) n - 1 ⁢ n n - 2 ( n - 1 ) ! ⁢ x n , Lambert-Wp 𝑥 superscript subscript 𝑛 1 superscript 1 𝑛 1 superscript 𝑛 𝑛 2 𝑛 1 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\mathrm{Wp}\left(x\right)=\sum_{n=1}^{\infty}(-1)^% {n-1}\frac{n^{n-2}}{(n-1)!}x^{n},}}
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    DLMF id
    DLMF:4.13.E5
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    constraint
    | x | < 1 e 𝑥 1 𝑒 {\displaystyle{\displaystyle|x|<\dfrac{1}{e}}}
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    Symbols used
    Q11233
    Defining formula
    Wp ⁡ ( x ) Lambert-Wp 𝑥 {\displaystyle{\displaystyle\mathrm{Wp}\left(\NVar{x}\right)}}
    xml-id
    C4.S13.p2.m8abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1dec
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    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ddec
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