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Fungrim entry: ec7f2d

atan⁡(z)=csgn⁡(z)acos⁡ ⁣(11+z2)\operatorname{atan}(z) = \operatorname{csgn}(z) \operatorname{acos}\!\left(\frac{1}{\sqrt{1 + {z}^{2}}}\right)
Assumptions:z∈C∖{−i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\operatorname{atan}(z) = \operatorname{csgn}(z) \operatorname{acos}\!\left(\frac{1}{\sqrt{1 + {z}^{2}}}\right)

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Definitions:
Fungrim symbol Notation Short description
Atanatan⁡(z)\operatorname{atan}(z) Inverse tangent
Csgncsgn⁡(z)\operatorname{csgn}(z) Real-valued sign function for complex numbers
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("ec7f2d"),
    Formula(Equal(Atan(z), Mul(Csgn(z), Acos(Div(1, Sqrt(Add(1, Pow(z, 2)))))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

Topics using this entry

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