DLMF:4.23.E21

MaRDI QIDQ2027

• Label: DLMF:4.23.E21

Digital Library of Mathematical Functions ID 4.23.E21

${\displaystyle{\displaystyle\operatorname{arcsin}x=-\tfrac{1}{2}\pi\pm i\ln\left((x^{2}-1)^{1/2}-x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\in(-\infty,-1]}}$

Symbols List

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

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