DLMF:4.37.E20 (Q1939)

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DLMF:4.37.E20
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    Statements

    Defining formula
    arccosh ⁡ ( i ⁢ y ) = ± 1 2 ⁢ π ⁢ i + ln ⁡ ( ( y 2 + 1 ) 1 / 2 ± y ) , hyperbolic-inverse-cosine imaginary-unit 𝑦 plus-or-minus 1 2 𝜋 imaginary-unit plus-or-minus superscript superscript 𝑦 2 1 1 2 𝑦 {\displaystyle{\displaystyle\operatorname{arccosh}\left(\mathrm{i}y\right)=\pm% \tfrac{1}{2}\pi\mathrm{i}+\ln\left((y^{2}+1)^{1/2}\pm y\right),}}
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    DLMF id
    DLMF:4.37.E20
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    constraint
    y ≷ 0 greater-than-or-less-than 𝑦 0 {\displaystyle{\displaystyle y\gtrless 0}}
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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.m2addec
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