Generating function of a_n * b_n

Question

I've been searching for the answer yet no luck. Please let me know if this is a duplicate.

Let $A(x) = \sum a_n x^n$, $B(x) = \sum b_n x^n$, $C(x) = \sum a_n b_n x^n$.

I am looking for the closed form of $C(x)$ in terms of $A(x)$ and $B(x)$.

Thanks in advance,

Best.