DLMF:2.1.E9 (Q693)

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DLMF:2.1.E9
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    Statements

    Defining formula
    e z = 1 + z + O ⁡ ( z 2 ) , superscript 𝑒 𝑧 1 𝑧 Big-O superscript 𝑧 2 {\displaystyle{\displaystyle e^{z}=1+z+O\left(z^{2}\right),}}
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    DLMF id
    DLMF:2.1.E9
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    constraint
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
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    z → 0 → 𝑧 0 {\displaystyle{\displaystyle z\to 0}}
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    ℂ ℂ {\displaystyle{\displaystyle\mathbb{C}}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2addec
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    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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