Bean starlike — φ(z) = √(1 + tanh z) - Family

Canonical Key

ma_minda_bean_tanh

Generating Definition

z f′(z)/f(z) ≺ φ(z) = √(1 + tanh z)

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

Unit disk explorer - hover to evaluate

Hover over the disk

Facts (0)

Property	Kind	Params	Holds	Value / r	Status	Confidence

Verification Runs (0)

Verifier	Property	Direction	Outcome	Domain r	Witness	Engine

Instances (1)

Papers in this φ-class (2)

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.

On Starlike Functions Associated with a Bean Shaped Domain high

S. Sivaprasad Kumar, Pooja Yadav · 2024

“S∗ B := {f ∈ S : zf′(z) f(z) ≺B(z) := √ 1 + tanh z }”

On estimation of Hankel determinants for certain class of starlike functions high

S. Sivaprasad Kumar, Neha Verma · 2024

“Class S*_B: f in A: zf'(z)/f(z) subordinate to sqrt(1 + tanh(z))”

✦ You're explorer #5,481 to wander the registry - thanks for stopping by. Tell us what you'd like to see →

💬 Feedback

Bean starlike — φ(z) = √(1 + tanh z)