z·exp(z⁴/4) (queue test)

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This function is certified starlike - the sharp, proven-exact coefficient bounds for the starlike class apply to it. See the certified proofs →

Canonical Key

z*exp(z**4/4)

Closed Form

f(z) = z*exp(z**4/4)

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

Radius of starlikeness r* ≈ 0.9990
proven f is starlike on |z| < r*; the colored disk shows the certified region.

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Facts (1)

Property	Kind	Params	Holds	Value / r	Status	Confidence
S*	membership	{}	✓	r ≤ 0.999	✓ proven	proven

Transitively Implied Properties

Because starlikeness is proven, these properties follow by classical implications (unconditional edges in the lattice):

Verification Runs (5)

Verifier	Property	Direction	Outcome	Domain r	Witness	Engine
boundary_scan_closed_form_v31	starlike	proves	pass	0.999	-	boundary_v3.1
boundary_scan_closed_form_v31	starlike	proves	pass	0.999	-	gft-0.1.0-reaudit-20260610
boundary_scan_centered_v31	starlike	proves	pass	0.999	-	tiered_v1.0
boundary_scan_closed_form_v31	starlike	proves	pass	0.999	-	tiered_v1.0
screen_grid_v1	starlike	proves	pass	0.950	-	tiered_v1.0

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

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Related

Facts (1)

Transitively Implied Properties

Verification Runs (5)

Instances (1)