Cauchy's Integral Formula/General Result/Corollary

Theorem
Let $G \left({z}\right)$ be the generating function for the sequence $\left\langle{a_n}\right\rangle$.

Let the coefficient of $z^n$ extracted from $G \left({z}\right)$ be denoted:
 * $\left[{z^n}\right] G \left({z}\right) := a_n$

Let $G \left({z}\right)$ be convergent for $z = z_0$ and $0 < r < \left\lvert{z_0}\right\rvert$.

Then:
 * $\left[{z^n}\right] G \left({z}\right) = \displaystyle \frac 1 {2 \pi i} \oint_{\left\lvert{z}\right\rvert \mathop = r} \dfrac {G \left({z}\right) \rd z} {z^{n + 1} }$