\[f_{n}-g_{n}=\frac{1}{2\pi i}\int_{|z|=r}\frac{f(z)-g(z)}{z^{n+1}}\,\mathrm{d}z%
=\frac{1}{2\pi r^{n}}\int_{0}^{2\pi}\left(f\left(re^{i\theta}\right)-g\left(re%
^{i\theta}\right)\right)e^{-ni\theta}\,\mathrm{d}\theta.\]