Sum over k of r Choose k by Minus r Choose m Minus 2k

Theorem
Let $r \in \R$, $m \in \Z$.


 * $\displaystyle \sum_{k \mathop \in \Z} \binom r k \binom {-r} {m - 2 k} \paren {-1}^{m + k} = \binom r m$

Proof
We have:

Thus we have:

Comparing the coefficients of $x^m$ on both sides yields the result.