Formula:2053

Digital Library of Mathematical Functions ID 4.23.E34

${\displaystyle{\displaystyle\operatorname{arcsin}z=\operatorname{arcsin}\beta+\mathrm{i}\operatorname{sign}\left(y\right)\ln\left(\alpha+(\alpha^{2}-1)^{1/2}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle[\NVar{a},\NVar{b}]}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\notin}}$:
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• ${\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle\alpha}}$: 4.23.E37
• ${\displaystyle{\displaystyle\beta}}$: 4.23.E38
 

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