Definition:Weierstrass Elementary Factor

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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


Source of Name

This entry was named for Karl Theodor Wilhelm Weierstrass.


Sources