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:


 * $E_n \left({z}\right) = \displaystyle \begin{cases} 1 - z & : n = 0 \\

\left({1 - z}\right) \exp \left({z + \dfrac {z^2} 2 + \cdots + \dfrac{z^n} n}\right) & : \text{otherwise}\end{cases}$

Also see

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