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Fungrim entry: ec7f2d

atan ⁣(z)=csgn ⁣(z)acos ⁣(11+z2)\operatorname{atan}\!\left(z\right) = \operatorname{csgn}\!\left(z\right) \operatorname{acos}\!\left(\frac{1}{\sqrt{1 + {z}^{2}}}\right)
Assumptions:zC{i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\operatorname{atan}\!\left(z\right) = \operatorname{csgn}\!\left(z\right) \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}\!\left(z\right) Inverse tangent
Csgncsgn ⁣(z)\operatorname{csgn}\!\left(z\right) 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.

2019-09-16 21:17:18.797188 UTC