DLMF:8.11.E14 (Q2587)

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DLMF:8.11.E14
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    Statements

    Defining formula
    e n ⁢ x = e n ⁢ ( n ⁢ x ) + ( n ⁢ x ) n n ! ⁢ S n ⁢ ( x ) , superscript 𝑒 𝑛 𝑥 subscript 𝑒 𝑛 𝑛 𝑥 superscript 𝑛 𝑥 𝑛 𝑛 subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle e^{nx}=e_{n}(nx)+\frac{(nx)^{n}}{n!}S_{n}(x),}}
    0 references
    DLMF id
    DLMF:8.11.E14
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11332
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1edec
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    Q11329
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1cdec
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    functions (locally)
    Defining formula
    e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}
    xml-id
    C8.S4.XMD1.m1adec
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