# Difference between revisions of "Meromorphic"

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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]] [[root | 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>. | 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]] [[root | 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>. | ||

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## Latest revision as of 16:41, 28 March 2009

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Let be a connected open set in the complex plane. A function on is said to be **meromorphic** if there are functions and which are holomorphic on , has isolated zeros and can be written as wherever .