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Difference between revisions of "Meromorphic"

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Let <math>D\subseteq\mathbb{C}</math> be a [[domain]] in the [[complex plane]]. A function on <math>D</math> is said to be '''meromorphic''' if it can be written as <math>f(z)=\frac{g(z)}{h(z)}</math> wherever <math>h(z)\neq 0</math>, where <math>g</math> and <math>h</math> are [[holomorphic]] on <math>D</math>. Furthermore, it is required that <math>h</math> have [[isolated point|isolated]] [[zero]]s.
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Let <math>D\subseteq\mathbb{C}</math> be a [[connected set|connected]] [[open set]] in the [[complex plane]]. A function <math>f</math> on <math>D</math> is said to be '''meromorphic''' if there are functions <math>g</math> and <math>h</math> which are [[holomorphic]] on <math>D</math>, <math>h</math> has [[isolated point|isolated]] [[zero]]s and <math>f</math> can be written as <math>f(z)=\frac{g(z)}{h(z)}</math> wherever <math>h(z)\neq 0</math>.

Revision as of 12:51, 14 August 2006

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Let $D\subseteq\mathbb{C}$ be a connected open set in the complex plane. A function $f$ on $D$ is said to be meromorphic if there are functions $g$ and $h$ which are holomorphic on $D$, $h$ has isolated zeros and $f$ can be written as $f(z)=\frac{g(z)}{h(z)}$ wherever $h(z)\neq 0$.

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