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Canonical Key
ma_minda_cosh

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* ≈ 0.800
Radius of starlikeness r* ≈ 0.8000
disproven f is starlike on |z| < r*; the colored disk shows the certified region.

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Related

Facts (4)

Property Kind Params Holds Value / r Status Confidence
K membership {} -6.1778 unscreened -
r* radius {} - r ≤ 0.865 🔬 screened numerical_strong
S* membership {} r ≤ 0.800 ✗ disproven proven
S membership {} - unscreened -

Verification Runs (3)

Verifier Property Direction Outcome Domain r Witness Engine
boundary_scan_centered_v31 starlike disproves pass 0.800 0.9*exp(i*1.59534) boundary_v3.1
pointwise_starlike_iv starlike disproves pass 0.990 [6.062001655779399e-17, 0.99] gft-0.1.0-reaudit-20260610
boundary_scan_closed_form starlike disproves pass 0.800 0.9*exp(i*1.546253) boundary_v3.0

Instances (1)

{}

Papers in this φ-class (1)

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.

Mridula Mundalia, S. Sivaprasad Kumar · 2022
“p(z) ≺ cosh √z, if and only if A ≤”
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