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Fungrim entry: a6cd13

HolomorphicDomain ⁣(atan ⁣(z),z,C{~})=C(,1]i[1,)i\operatorname{HolomorphicDomain}\!\left(\operatorname{atan}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C} \setminus \left(-\infty, -1\right] i \cup \left[1, \infty\right) i
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] i \cup \left[1, \infty\right) i
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
CCC\mathbb{C} Complex numbers
UnsignedInfinity~{\tilde \infty} Unsigned infinity
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
ConstIii Imaginary unit
ClosedOpenInterval[a,b)\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(Mul(OpenClosedInterval(Neg(Infinity), -1), ConstI), Mul(ClosedOpenInterval(1, Infinity), ConstI))))))

Topics using this entry

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

2019-09-16 21:17:18.797188 UTC