DLMF:4.37.E14 (Q1933)

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DLMF:4.37.E14
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    Statements

    Defining formula
    arcsech ⁡ ( - z ) = ∓ π ⁢ i + arcsech ⁡ z , hyperbolic-inverse-secant 𝑧 minus-or-plus 𝜋 𝑖 hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\left(-z\right)=\mp\pi i+% \operatorname{arcsech}z,}}
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    DLMF id
    DLMF:4.37.E14
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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.m2aadec
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    inverse hyperbolic secant function
    Defining formula
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2abdec
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    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2aadec
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