\begin{definition}[Definition:Multiplication of Polynomials/Sequence]
Let:
: $f = \sequence {a_k} = \tuple {a_0, a_1, a_2, \ldots}$
and:
: $g = \sequence {b_k} = \tuple {b_0, b_1, b_2, \ldots}$
be polynomials over a field $F$.
Then the operation of '''(polynomial) multiplication''' is defined as:
:$f g := \tuple {c_0, c_1, c_2, \ldots}$
where $\ds c_i = \sum_{j \mathop + k \mathop = i} a_j b_k$
\end{definition}