Formula:2351

Digital Library of Mathematical Functions ID 4.37.E16

${\displaystyle{\displaystyle\operatorname{arcsinh}z=\ln\left((z^{2}+1)^{1/2}+z\right),}}$

Constraint(s)

${\displaystyle{\displaystyle z/i\in\mathbb{C}\setminus(-\infty,-1)\cup(1,\infty)}}$

Symbols List

• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• ${\displaystyle{\displaystyle\setminus}}$:
• ${\displaystyle{\displaystyle\cup}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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