7 problems.
- \(-\frac12\bigl(z+\frac1z\bigr)\) maps the upper half-disk conformally onto the upper half-plane
- \(P_n(z)=\sum_{k=1}^n kz^{k-1}\) has no zeros in \(|z|<r<1\) for large \(n\)
- Dense values near an accumulation point of poles, versus Casorati–Weierstrass
- An entire function sending a circle into \(\mathbb{R}\) is constant
- \(\frac1\pi\iint_{\mathbb{D}}|\psi_\alpha'|^2=1\) and \(\frac1\pi\iint_{\mathbb{D}}|\psi_\alpha'|=\frac{1-|\alpha|^2}{|\alpha|^2}\log\frac1{1-|\alpha|^2}\) for \(\psi_\alpha(z)=\frac{\alpha-z}{1-\bar\alpha z}\)
- Conformal maps from circular lunes, slit discs, and half-discs
- Blaschke-factor integral identities and a half-disk conformal map