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Canonical Key
z+2*z**2
Closed Form
f(z) = z + 2z^2

Image domain \(f(\mathbb{D})\)

The image of the unit disk under \(f\): concentric circles \(|z|=r\) and radial spokes mapped through \(f(z)=z+a_2z^2+\dots\); the bold curve is the boundary \(f(e^{i\theta})\). Rendered in your browser from the certified Taylor coefficients - nothing is computed server-side.

Taylor series
r* ≈ 0.000
Radius of starlikeness r* ≈ 0.0000
disproven f is starlike on |z| < r*; the colored disk shows the certified region.

Unit disk explorer - hover to evaluate

Hover over the disk

Related

Facts (4)

Property Kind Params Holds Value / r Status Confidence
K membership {} -189.3462 unscreened -
r* radius {} - r ≤ 0.960 🔬 screened numerical_strong
S* membership {} r ≤ 0.000 ✗ disproven proven
S membership {} - unscreened -

Verification Runs (3)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_centered_v31 starlike disproves pass 0.000 - boundary_v3.1
pointwise_starlike_iv starlike disproves pass 0.492 [-0.4923529411764705, 6.029584534625496e-17] gft-0.1.0-reaudit-20260610
boundary_scan_polynomial starlike disproves pass 0.000 0.3*exp(i*3.239767) boundary_v3.0

Instances (1)

{}
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