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. | + | 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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Revision as of 02:06, 29 June 2006
Let 
be a domain in the complex plane. A function on 
is said to be meromorphic if it can be written as 
wherever 
, where 
and 
are holomorphic on . Furthermore, it is required that have isolated zeros.
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