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Canonical Key
z*(z**2/3-z/2+1)
Closed Form
f(z) = z - z**2/2 + z**3/3

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* ≈ 0.990
Radius of starlikeness r* ≈ 0.9900
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 (1)

Property Kind Params Holds Value / r Status Confidence
S* membership {} r ≤ 0.990 ✗ disproven proven

Verification Runs (3)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_closed_form_v31 starlike disproves pass 0.990 0.999*exp(i*1.119806) boundary_v3.1
boundary_scan_centered_v31 starlike disproves pass 0.990 0.999*exp(i*1.119806) gft-0.1.0-reaudit-20260610
boundary_scan_closed_form starlike disproves pass 0.990 0.999*exp(i*1.119806) boundary_v3.0

Instances (1)

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