DLMF:4.23.E26 (Q1778)

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DLMF:4.23.E26
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    Statements

    Defining formula
    arctan ⁡ z = i 2 ⁢ ln ⁡ ( i + z i - z ) , 𝑧 𝑖 2 𝑖 𝑧 𝑖 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}z=\frac{i}{2}\ln\left(\frac{i% +z}{i-z}\right),}}
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    DLMF id
    DLMF:4.23.E26
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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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