ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Empty map
Collection
Ring element collection
Ring element combination
Standard formal finite combination
Polynomial map
Polynomial function
Definition D4312
Complex polynomial function
Formulation 1
Let $r_0, r_1, \ldots, r_N \in \mathbb{C}$ each be a D1207: Complex number.
The complex polynomial function with respect to $r_0, r_1, \ldots, r_N$ is the D4881: Complex function \begin{equation} \mathbb{C} \to \mathbb{C}, \quad z \mapsto \sum_{n = 0}^N r_n z^n \end{equation}
Children
Monic complex polynomial function
Results
Strong fundamental theorem of complex algebra for a quadratic complex polynomial
Conjectures
Sendov's conjecture