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Fungrim entry: 90a864

atan ⁣(z)=0z11+t2dt\operatorname{atan}\!\left(z\right) = \int_{0}^{z} \frac{1}{1 + {t}^{2}} \, dt
Assumptions:zCandiz(,1][1,)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)
TeX:
\operatorname{atan}\!\left(z\right) = \int_{0}^{z} \frac{1}{1 + {t}^{2}} \, dt

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right] \cup \left[1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Integralabf ⁣(x)dx\int_{a}^{b} f\!\left(x\right) \, dx Integral
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Source code for this entry:
Entry(ID("90a864"),
    Formula(Equal(Atan(z), Integral(Div(1, Add(1, Pow(t, 2))), Tuple(t, 0, z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(Mul(ConstI, z), Union(OpenClosedInterval(Neg(Infinity), -1), ClosedOpenInterval(1, Infinity))))))

Topics using this entry

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

2019-09-19 20:12:49.583742 UTC