Normalized univalent function
= Normalized univalent function
{title2=$\mathcal S=\{f:\mathbb D\to\mathbb C\text{ univalent},\ f(0)=0,\ f'(0)=1\}$}
A <normalized univalent function> is a <holomorphic function> on the <unit disc> which is <injective> and has the displayed normalization. Its <Taylor series> begins $z+a_2z^2+\cdots$. Normalization makes coefficient bounds and image-size estimates independent of translation and dilation; the <Koebe quarter theorem> is the sharp universal image bound.