差分

:$$G_n=\displaystyle\frac{z^n-\overline{z}^{~n}}{z-\overline{z}}=\frac{2i\sin\left(n~\mathrm{Arg}~z^n\right)}{2i\sin\left(\mathrm{Arg}~z\right)}=\frac{\sin\left(n~\mathrm{Arg}~z^n\right)}{\sin\left(\mathrm{Arg}~z\right)}$$