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Fungrim entry: 4e5947

atan ⁣(z)=k=0(1)kz2k+12k+1\operatorname{atan}\!\left(z\right) = \sum_{k=0}^{\infty} \frac{{\left(-1\right)}^{k} {z}^{2 k + 1}}{2 k + 1}
Assumptions:zCandz<1z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 1
TeX:
\operatorname{atan}\!\left(z\right) = \sum_{k=0}^{\infty} \frac{{\left(-1\right)}^{k} {z}^{2 k + 1}}{2 k + 1}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \left|z\right| < 1
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Sumnf ⁣(n)\sum_{n} f\!\left(n\right) Sum
Powab{a}^{b} Power
Infinity\infty Positive infinity
CCC\mathbb{C} Complex numbers
Absz\left|z\right| Absolute value
Source code for this entry:
Entry(ID("4e5947"),
    Formula(Equal(Atan(z), Sum(Div(Mul(Pow(-1, k), Pow(z, Add(Mul(2, k), 1))), Add(Mul(2, k), 1)), Tuple(k, 0, Infinity)))),
    Variables(z),
    Assumptions(And(Element(z, CC), Less(Abs(z), 1))))

Topics using this entry

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

2019-09-20 18:07:53.062439 UTC