Chu-Vandermonde Identity/Extended

Theorem
Let $r, s, \alpha, \beta \in \C$ be complex numbers.

Then:
 * $\ds \sum_{k \mathop \in \Z} \dbinom r {\alpha + k} \dbinom s {\beta - k} = \dbinom {r + s} {\alpha + \beta}$

where $\dbinom r {\alpha + k}$ denotes a binomial coefficient.