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Fungrim entry: 67c0be

atan⁡ ⁣(z)=2atan⁡ ⁣(z1+1+z2)\operatorname{atan}\!\left(z\right) = 2 \operatorname{atan}\!\left(\frac{z}{1 + \sqrt{1 + {z}^{2}}}\right)
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{atan}\!\left(z\right) = 2 \operatorname{atan}\!\left(\frac{z}{1 + \sqrt{1 + {z}^{2}}}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Atanatan⁡ ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("67c0be"),
    Formula(Equal(Atan(z), Mul(2, Atan(Div(z, Add(1, Sqrt(Add(1, Pow(z, 2))))))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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

2019-06-18 07:49:59.356594 UTC