Definition:Polynomial Function/Complex

Definition
Let $a_0, \ldots a_n \in \C$.

Then for all $x \in \C$, the expression:
 * $\forall z \in \C: \displaystyle P \left({x}\right) = \sum_{j \mathop = 0}^n \left({a_j z^j}\right) = a_0 + a_1 z + a_2 z^2 + \cdots + a_{n-1} z^{n-1} + a_n z^n$

defines a complex function from $\C$ to $\C$.

This is known as a (complex) polynomial function.

Coefficients
The parameters $a_0, \ldots a_n \in \C$ are known as the coefficients of the polynomial $P$.

Also see

 * Complex Polynomial Function is Complex Function


 * Definition:Real Polynomial Function


 * Definition:Polynomial over Real Numbers
 * Definition:Polynomial over Complex Numbers