How can I simplify the following expression?
$$\sum_{j=0}^{k} \binom{n-j}{p} \binom{m+j}{q}$$
where $n,m,p,q,k$ are positive constants such that $n-k \ge p$ and $m \ge q$.
How can I simplify the following expression?
$$\sum_{j=0}^{k} \binom{n-j}{p} \binom{m+j}{q}$$
where $n,m,p,q,k$ are positive constants such that $n-k \ge p$ and $m \ge q$.