DLMF:4.23.E22 (Q1774)

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DLMF:4.23.E22
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    Statements

    test
    arccos ⁡ z = 1 2 ⁢ π + i ⁢ ln ⁡ ( ( 1 - z 2 ) 1 / 2 + i ⁢ z ) , 𝑧 1 2 𝜋 𝑖 superscript 1 superscript 𝑧 2 1 2 𝑖 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}z=\tfrac{1}{2}\pi+i\ln\left((% 1-z^{2})^{1/2}+iz\right),}}
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    DLMF id
    DLMF:4.23.E22
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    constraint
    z ∈ ℂ ∖ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1)\cup(1,\infty)}}
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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.m2agdec
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