DLMF:4.37.E16 (Q1935)

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DLMF:4.37.E16
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    Statements

    test
    arcsinh ⁡ z = ln ⁡ ( ( z 2 + 1 ) 1 / 2 + z ) , hyperbolic-inverse-sine 𝑧 superscript superscript 𝑧 2 1 1 2 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}z=\ln\left((z^{2}+1)^{1/2}+z% \right),}}
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    DLMF id
    DLMF:4.37.E16
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    constraint
    z / i ∈ ℂ ∖ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) 𝑧 𝑖 1 1 {\displaystyle{\displaystyle z/i\in\mathbb{C}\setminus(-\infty,-1)\cup(1,% \infty)}}
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    Symbols used
    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
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