Formula:2057

Digital Library of Mathematical Functions ID 4.23.E36

${\displaystyle{\displaystyle\operatorname{arctan}z=\tfrac{1}{2}\operatorname{arctan}\left(\frac{2x}{1-x^{2}-y^{2}}\right)+\tfrac{1}{4}i\ln\left(\frac{x^{2}+(y+1)^{2}}{x^{2}+(y-1)^{2}}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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