Definition:Multiplication of Polynomials/Sequence

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