Cauchy's Integral Formula/General Result/Corollary

Theorem
Let $\map G z$ be the generating function for the sequence $\sequence {a_n}$.

Let the coefficient of $z^n$ extracted from $\map G z$ be denoted:
 * $\sqbrk {z^n} \map G z := a_n$

Let $\map G z$ be convergent for $z = z_0$ and $0 < r < \cmod {z_0}$.

Then:
 * $\sqbrk {z^n} \map G z = \displaystyle \frac 1 {2 \pi i} \oint_{\cmod z \mathop = r} \dfrac {\map G z \d z} {z^{n + 1} }$