Difference between revisions of "Weierstrass elementary factors"
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(Created page with "The Weierstrass elementary factors $E_n$ are defined for $n \in \{0,1,2,\ldots\}$ by $$E_n(z)=\left\{ \begin{array}{ll} 1-z &; n=0 \\ (1-z)e^{z+\frac{z^2}{2}+\frac{z^3}{3}+\ld...") |
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The Weierstrass elementary factors $E_n$ are defined for $n \in \{0,1,2,\ldots\}$ by | The Weierstrass elementary factors $E_n$ are defined for $n \in \{0,1,2,\ldots\}$ by | ||
$$E_n(z)=\left\{ \begin{array}{ll} | $$E_n(z)=\left\{ \begin{array}{ll} | ||
1-z &; n=0 \\ | 1-z &; n=0 \\ | ||
(1-z)e^{z+\frac{z^2}{2}+\frac{z^3}{3}+\ldots+\frac{z^n}{n}} &; \mathrm{otherwise}. \end{array} \right.$$ | (1-z)e^{z+\frac{z^2}{2}+\frac{z^3}{3}+\ldots+\frac{z^n}{n}} &; \mathrm{otherwise}. \end{array} \right.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Weierstrass elementary factors inequality]]<br /> | ||
| + | [[Product of Weierstrass elementary factors is entire]]<br /> | ||
| + | [[Weierstrass factorization theorem]]<br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 19:31, 26 November 2016
The Weierstrass elementary factors $E_n$ are defined for $n \in \{0,1,2,\ldots\}$ by $$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
