Formula:2039

Digital Library of Mathematical Functions ID 4.23.E27

${\displaystyle{\displaystyle\operatorname{arctan}\left(iy\right)=\pm\frac{1}{2}\pi+\frac{i}{2}\ln\left(\frac{y+1}{y-1}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle y\in(-\infty,-1)\cup(1,\infty)}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• ${\displaystyle{\displaystyle\cup}}$:
• ${\displaystyle{\displaystyle y}}$: real variable
 

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