DLMF:4.23.E27 (Q1779)

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DLMF:4.23.E27
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    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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