Definition:Weierstrass Elementary Factor

Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.

The $n$th (Weierstrass) elementary factor is the function $E_n: \C \to \C$ defined as:


 * $\map {E_n} z = \begin {cases} 1 - z & : n = 0 \\

\paren {1 - z} \map \exp {z + \dfrac {z^2} 2 + \cdots + \dfrac{z^n} n} & : \text{otherwise} \end {cases}$

Also see

 * Bounds for Weierstrass Elementary Factors, which motivates their definition
 * Weierstrass Factorization Theorem