Say I have a product, $\sum_{n=0}^{+\infty} \sum_{k=0}^{+\infty}q_{n}r_{k}\delta_{n-1,k-1}$. How do I evaluate this?
I've tried opening up the $n$ summation, which gives me, $\sum_{k=0}^{+\infty} \left( q_{0} r_{k} \delta_{-1, k-1} + q_{1} r_{k} \delta_{0, k - 1} + \cdots \right)$. I'm at a loss as to how to proceed further.
Any help would be highly appreciated.