DLMF:4.2.E33 (Q1573)

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DLMF:4.2.E33
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    Statements

    DLMF defining formula
    e z = ( exp ⁡ z ) ⁢ exp ⁡ ( 2 ⁢ k ⁢ z ⁢ π ⁢ i ) , superscript 𝑒 𝑧 𝑧 2 𝑘 𝑧 𝜋 imaginary-unit {\displaystyle{\displaystyle e^{z}=(\exp z)\exp\left(2kz\pi\mathrm{i}\right),}}
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    constraint
    k ∈ ℤ 𝑘 {\displaystyle{\displaystyle k\in\mathbb{Z}}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2akdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    Q10792
    DLMF defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1bdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1zdec
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    Identifiers

     
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