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Fungrim entry: a6cd13

atan(z) is holomorphic on zC((,1]i[1,)i)\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
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
Atanatan(z)\operatorname{atan}(z) Inverse tangent
CCC\mathbb{C} Complex numbers
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(IsHolomorphic(Atan(z), ForElement(z, SetMinus(CC, Parentheses(Union(Mul(OpenClosedInterval(Neg(Infinity), -1), ConstI), Mul(ClosedOpenInterval(1, Infinity), ConstI))))))))

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

2020-01-31 18:09:28.494564 UTC