Formula:2359

Digital Library of Mathematical Functions ID 4.37.E20

${\displaystyle{\displaystyle\operatorname{arccosh}\left(\mathrm{i}y\right)=\pm\tfrac{1}{2}\pi\mathrm{i}+\ln\left((y^{2}+1)^{1/2}\pm y\right),}}$

Constraint(s)

${\displaystyle{\displaystyle y\gtrless 0}}$

Symbols List

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

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