Fungrim entry: a6cd13

\operatorname{atan}(z) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(\left(-\infty, -1\right] i \cup \left[1, \infty\right) i\right)

TeX:

\operatorname{atan}(z) \text{ is holomorphic on } z \in \mathbb{C} \setminus \left(\left(-\infty, -1\right] i \cup \left[1, \infty\right) i\right)

Definitions:

Fungrim symbol	Notation	Short description
`IsHolomorphic`	$f(z) \text{ is holomorphic at } z = c$	Holomorphic predicate
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity
`ConstI`	$i$	Imaginary unit
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval

Source code for this entry:

Entry(ID("a6cd13"),
    Formula(IsHolomorphic(Atan(z), ForElement(z, SetMinus(CC, Parentheses(Union(Mul(OpenClosedInterval(Neg(Infinity), -1), ConstI), Mul(ClosedOpenInterval(1, Infinity), ConstI))))))))

Topics using this entry

Inverse tangent

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC