Fungrim entry: 40baa9

$\mathcal{E}_{\rho} = \left\{ \frac{\rho {e}^{i \theta} + {\rho}^{-1} {e}^{-i \theta}}{2} : \theta \in \left[0, 2 \pi\right) \right\}$
Assumptions:$\rho \in \mathbb{R} \,\mathbin{\operatorname{and}}\, \rho > 1$
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
BernsteinEllipse$\mathcal{E}_{\rho}$ Bernstein ellipse with foci -1,+1 and semi-axis sum rho
Exp${e}^{z}$ Exponential function
ConstI$i$ Imaginary unit
Pow${a}^{b}$ Power
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Pi$\pi$ The constant pi (3.14...)
RR$\mathbb{R}$ Real numbers
Source code for this entry:
Entry(ID("40baa9"),
Formula(Equal(BernsteinEllipse(rho), Set(Div(Add(Mul(rho, Exp(Mul(ConstI, theta))), Mul(Pow(rho, -1), Exp(Neg(Mul(ConstI, theta))))), 2), ForElement(theta, ClosedOpenInterval(0, Mul(2, Pi)))))),
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.

2019-12-11 23:01:54.699850 UTC