Difference between revisions of "Weierstrass elementary factors"
From specialfunctionswiki
| (One intermediate revision by the same user not shown) | |||
| Line 7: | Line 7: | ||
=Properties= | =Properties= | ||
[[Weierstrass elementary factors inequality]]<br /> | [[Weierstrass elementary factors inequality]]<br /> | ||
| − | + | [[Product of Weierstrass elementary factors is entire]]<br /> | |
| − | |||
[[Weierstrass factorization theorem]]<br /> | [[Weierstrass factorization theorem]]<br /> | ||
Latest revision as of 19:31, 26 November 2016
The Weierstrass elementary factors $E_n$ are defined for $n \in \{0,1,2,\ldots\}$ by $$E_n(z)=\left\{ \begin{array}{ll} 1-z &; n=0 \\ (1-z)e^{z+\frac{z^2}{2}+\frac{z^3}{3}+\ldots+\frac{z^n}{n}} &; \mathrm{otherwise}. \end{array} \right.$$
Properties
Weierstrass elementary factors inequality
Product of Weierstrass elementary factors is entire
Weierstrass factorization theorem
