DLMF:4.8.E6 (Q1597)

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DLMF:4.8.E6
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    Statements

    Defining formula
    ln ⁡ ( z n ) = n ⁢ ln ⁡ z , superscript 𝑧 𝑛 𝑛 𝑧 {\displaystyle{\displaystyle\ln\left(z^{n}\right)=n\ln z,}}
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    DLMF id
    DLMF:4.8.E6
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    constraint
    n ∈ ℤ 𝑛 {\displaystyle{\displaystyle n\in\mathbb{Z}}}
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    - π ≤ n ⁢ ph ⁡ z ≤ π 𝜋 𝑛 phase 𝑧 𝜋 {\displaystyle{\displaystyle-\pi\leq n\operatorname{ph}z\leq\pi}}
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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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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    Q10818
    Defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.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.m2abdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1edec
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