Formula:2353

Digital Library of Mathematical Functions ID 4.37.E17

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

Constraint(s)

${\displaystyle{\displaystyle y\in[1,\infty)}}$

Symbols List

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

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