DLMF:4.8.E11 (Q1602)

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DLMF:4.8.E11
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    Statements

    test
    Ln ⁡ ( a z ) = z ⁢ Ln ⁡ a + 2 ⁢ k ⁢ π ⁢ i , multivalued-natural-logarithm superscript 𝑎 𝑧 𝑧 multivalued-natural-logarithm 𝑎 2 𝑘 𝜋 imaginary-unit {\displaystyle{\displaystyle\operatorname{Ln}\left(a^{z}\right)=z\operatorname% {Ln}a+2k\pi\mathrm{i},}}
    0 references
    DLMF id
    DLMF:4.8.E11
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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
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q10818
    test
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2acdec
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    general logarithm function
    test
    Ln ⁡ z multivalued-natural-logarithm 𝑧 {\displaystyle{\displaystyle\operatorname{Ln}\NVar{z}}}
    xml-id
    C4.S2.E1.m2aedec
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    Q11219
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1adec
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    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1dec
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    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1jdec
    0 references
     
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