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Fungrim entry: 40baa9

Eρ={ρeiθ+ρ1eiθ2:θ[0,2π)}\mathcal{E}_{\rho} = \left\{ \frac{\rho {e}^{i \theta} + {\rho}^{-1} {e}^{-i \theta}}{2} : \theta \in \left[0, 2 \pi\right) \right\}
Assumptions:ρRandρ>1\rho \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \rho > 1
TeX:
\mathcal{E}_{\rho} = \left\{ \frac{\rho {e}^{i \theta} + {\rho}^{-1} {e}^{-i \theta}}{2} : \theta \in \left[0, 2 \pi\right) \right\}

\rho \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \rho > 1
Definitions:
Fungrim symbol Notation Short description
BernsteinEllipseEρ\mathcal{E}_{\rho} Bernstein ellipse with foci -1,+1 and semi-axis sum rho
SetBuilder{f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Powab{a}^{b} Power
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
ConstPiπ\pi The constant pi (3.14...)
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("40baa9"),
    Formula(Equal(BernsteinEllipse(rho), SetBuilder(Div(Add(Mul(rho, Exp(Mul(ConstI, theta))), Mul(Pow(rho, -1), Exp(Neg(Mul(ConstI, theta))))), 2), theta, Element(theta, ClosedOpenInterval(0, Mul(2, ConstPi)))))),
    Variables(rho),
    Assumptions(And(Element(rho, RR), Greater(rho, 1))))

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

2019-09-22 15:43:45.410764 UTC