Definition:Multiplication of Polynomials/Sequence

Definition
Let:
 * $f = \left \langle {a_k}\right \rangle = \left({a_0, a_1, a_2, \ldots}\right)$

and:
 * $g = \left \langle {b_k}\right \rangle = \left({b_0, b_1, b_2, \ldots}\right)$

be polynomials over a field $F$.

Then the operation of (polynomial) multiplication is defined as:
 * $f g := \left({c_0, c_1, c_2, \ldots}\right)$

where $\displaystyle c_i = \sum_{j \mathop + k \mathop = i} a_j b_k$