DLMF:4.37.E11 (Q1930)

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DLMF:4.37.E11
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    Statements

    Defining formula
    arccosh ⁡ ( - z ) = ± π ⁢ i + arccosh ⁡ z , hyperbolic-inverse-cosine 𝑧 plus-or-minus 𝜋 𝑖 hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\left(-z\right)=\pm\pi i+% \operatorname{arccosh}z,}}
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    DLMF id
    DLMF:4.37.E11
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    constraint
    ℑ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Im z\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.m2adec
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    Q11246
    Defining formula
    arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9abdec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1kdec
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