DLMF:4.23.E27 (Q2039)

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DLMF:4.23.E27
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    Statements

    DLMF defining formula
    arctan ⁡ ( i ⁢ y ) = ± 1 2 ⁢ π + i 2 ⁢ ln ⁡ ( y + 1 y - 1 ) , 𝑖 𝑦 plus-or-minus 1 2 𝜋 𝑖 2 𝑦 1 𝑦 1 {\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=\pm\frac{1}{2% }\pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right),}}
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    constraint
    y ∈ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) 𝑦 1 1 {\displaystyle{\displaystyle y\in(-\infty,-1)\cup(1,\infty)}}
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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.m2aidec
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    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2ahdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aldec
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    Q10790
    DLMF defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7aedec
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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.m2ahdec
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    Q10751
    DLMF defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6acdec
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    Q10798
    DLMF defining formula
    ∪ {\displaystyle{\displaystyle\cup}}
    xml-id
    introduction.Sx4.p1.t1.r28.m2addec
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    real variable
    DLMF defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1dec
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    Identifiers

     
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