序号

图形表示

保形映射

①

$\omega =\frac{R\left(z^2-1\right)}{z^2+1}=\frac{R\left(z^{\frac{\pi /2}{\pi /4}}-1\right)}{z^{\frac{\pi /2}{\pi /4}}+1}$

②

$\omega =\frac{R\left(z^{\frac{3}{2}}-1\right)}{z^{\frac{3}{2}}+1}=\frac{R\left(z^{\frac{\pi /2}{\pi /3}}-1\right)}{z^{\frac{\pi /2}{\pi /3}}+1}$

③

$\omega =\frac{R\left(z^3-1\right)}{z^3+1}=\frac{R\left(z^{\frac{\pi /2}{\pi /6}}-1\right)}{z^{\frac{\pi /2}{\pi /6}}+1}$

④

$\omega =\frac{R\left(z^{\frac{\pi /2}{\alpha }}-1\right)}{z^{\frac{\pi /2}{\alpha }}+1}=\frac{R\left(z^{\frac{\pi }{2\alpha }}-1\right)}{z^{\frac{\pi }{2\alpha }}+1}$