Formula:2385

Digital Library of Mathematical Functions ID 4.38.E2

${\displaystyle{\displaystyle\operatorname{arcsinh}z=\ln\left(2z\right)+\frac{1}{2}\frac{1}{2z^{2}}-\frac{1\cdot 3}{2\cdot 4}\frac{1}{4z^{4}}+\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\frac{1}{6z^{6}}-\cdots,}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z>0}}$
${\displaystyle{\displaystyle\Re z>0}}$
${\displaystyle{\displaystyle|z|>1}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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