Fungrim entry: a6cd13

\operatorname{HolomorphicDomain}\!\left(\operatorname{atan}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, -1\right] \cup \left[1, \infty\right)

TeX:

\operatorname{HolomorphicDomain}\!\left(\operatorname{atan}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, -1\right] \cup \left[1, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`CC`	$\mathbb{C}$	Complex numbers
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval

Source code for this entry:

Entry(ID("a6cd13"),
    Formula(Equal(HolomorphicDomain(Atan(z), z, Union(CC, Set(UnsignedInfinity))), SetMinus(CC, Union(OpenClosedInterval(Neg(Infinity), -1), ClosedOpenInterval(1, Infinity))))))

Topics using this entry

Inverse tangent