This function is certified starlike - the
sharp, proven-exact coefficient bounds for the starlike class apply to it.
See the certified proofs →
Canonical Key
ma_minda_cardioid
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.
Because starlikeness is proven, these properties follow by classical implications (unconditional edges in the lattice):
SC
Verification Runs (2)
Verifier
Property
Direction
Outcome
Domain r
Witness
Engine
boundary_scan_centered_v31
starlike
proves
pass
0.999
-
boundary_v3.1
boundary_scan_polynomial
starlike
proves
pass
0.999
-
boundary_v3.0
Instances (1)
{}
Papers in this φ-class (15)
Papers that explicitly study S*(φ) for this φ - conservatively tagged from the corpus
(explicit φ formula, class symbol, or unambiguous name). Quote = the supporting passage.