Definition:Polynomial/Real Numbers

Definition
A polynomial (in $\R$) is an expression of the form:


 * $\displaystyle P \left({x}\right) = \sum_{j \mathop = 0}^n \left({a_j x^j}\right) = a_0 + a_1 x + a_2 x^2 + \cdots + a_{n-1} x^{n-1} + a_n x^n$

where:
 * $x \in \R$
 * $a_0, \ldots a_n \in \mathbb k$ where $\mathbb k$ is one of the standard number sets $\Z, \Q, \R$.

Real Polynomial Function
In real analysis, this concept is usually encountered as a (real) polynomial function:

Complex Polynomial Function
Similarly, in complex analysis, this concept is usually encountered as a (complex) polynomial function: