7 problems.
- Holomorphy of both \(f(z)\) and \(f(\bar{z})\) on the disk forces \(f\) constant
- The integral \(\int_\gamma F(w)/(w-z)\,dw\) is holomorphic off \(\gamma\)
- The integral \(\int_0^\infty\frac{1}{1+x^n}\,dx\) by a wedge of angle \(\frac{2\pi}{n}\)
- \((1+z/n)^n\) converges uniformly to \(e^z\) on compact subsets of \(\mathbb{C}\)
- An entire function of modulus \(1\) on the unit circle is \(e^{i\theta}z^n\)
- \(\bigl|\frac{f(z)-f(0)}{M^2-\overline{f(0)}f(z)}\bigr|\le\frac{|z|}{MR}\) for \(|f|\le M\) on \(D(0,R)\)
- Conformal map from the intersection of \(|z-1|<2\) and \(|z+1|<2\) to the upper half-plane