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Fungrim entry: 34ff28

atan⁡(z)=z 2F1 ⁣(1,12,32,−z2)\operatorname{atan}(z) = z \,{}_2F_1\!\left(1, \frac{1}{2}, \frac{3}{2}, -{z}^{2}\right)
Assumptions:z∈C∖{−i,i}z \in \mathbb{C} \setminus \left\{-i, i\right\}
TeX:
\operatorname{atan}(z) = z \,{}_2F_1\!\left(1, \frac{1}{2}, \frac{3}{2}, -{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
Hypergeometric2F1 2F1 ⁣(a,b,c,z)\,{}_2F_1\!\left(a, b, c, z\right) Gauss hypergeometric function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
Source code for this entry:
Entry(ID("34ff28"),
    Formula(Equal(Atan(z), Mul(z, Hypergeometric2F1(1, Div(1, 2), Div(3, 2), Neg(Pow(z, 2)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

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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