DLMF:4.2.E6 (Q1502)

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DLMF:4.2.E6
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    Statements

    Defining formula
    Ln ⁡ z = ln ⁡ z + 2 ⁢ k ⁢ π ⁢ i , multivalued-natural-logarithm 𝑧 𝑧 2 𝑘 𝜋 imaginary-unit {\displaystyle{\displaystyle\operatorname{Ln}z=\ln z+2k\pi\mathrm{i},}}
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    DLMF id
    DLMF:4.2.E6
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
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    general logarithm function
    Defining formula
    Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    xml-id
    C4.S2.E1.m2aadec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
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    Q11219
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1dec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1fdec
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