\begin{definition}[Definition:Binomial Coefficient/Complex Numbers]
Let $z, w \in \C$.
Then $\dbinom z w$ is defined as:
:$\dbinom z w := \ds \lim_{\zeta \mathop \to z} \lim_{\omega \mathop \to w} \dfrac {\map \Gamma {\zeta + 1} } {\map \Gamma {\omega + 1} \map \Gamma {\zeta - \omega + 1} }$
where $\Gamma$ denotes the Gamma function.
When $z$ is a negative integer and $w$ is not an integer, $\dbinom z w$ is infinite.
\end{definition}