DLMF:4.23.E21 (Q2027)

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DLMF:4.23.E21
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    Statements

    DLMF defining formula
    arcsin ⁡ x = - 1 2 ⁢ π ± i ⁢ ln ⁡ ( ( x 2 - 1 ) 1 / 2 - x ) , 𝑥 plus-or-minus 1 2 𝜋 𝑖 superscript superscript 𝑥 2 1 1 2 𝑥 {\displaystyle{\displaystyle\operatorname{arcsin}x=-\tfrac{1}{2}\pi\pm i\ln% \left((x^{2}-1)^{1/2}-x\right),}}
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    constraint
    x ∈ ( - ∞ , - 1 ] 𝑥 1 {\displaystyle{\displaystyle x\in(-\infty,-1]}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    Q11213
    DLMF defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5afdec
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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Q11215
    DLMF defining formula
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3adec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1adec
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    Identifiers

     
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