DLMF:4.2.E7 (Q1503)

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DLMF:4.2.E7
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    Statements

    test
    ln ⁡ ( x ± i ⁢ 0 ) = ln ⁡ | x | ± i ⁢ π , plus-or-minus 𝑥 imaginary-unit 0 plus-or-minus 𝑥 𝑖 𝜋 {\displaystyle{\displaystyle\ln\left(x\pm\mathrm{i}0\right)=\ln|x|\pm i\pi,}}
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    DLMF id
    DLMF:4.2.E7
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    constraint
    - ∞ < x < 0 𝑥 0 {\displaystyle{\displaystyle-\infty<x<0}}
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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.m2acdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
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    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aedec
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    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1adec
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