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ANSWER

rouche

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Definitions of rouche in various dictionaries:

noun - a pleated strip of fine fabric

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Rouche might refer to
Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region * * * * K * * * {\displaystyle K} * with closed contour * * * * * K * * * {\displaystyle \partial K} * , if \|g(z)\| < \|f(z)\| on * * * * * K * * * {\displaystyle \partial K} * , then f and f + g have the same number of zeros inside * * * * K * * * {\displaystyle K} * , where each zero is counted as many times as its multiplicity. This theorem assumes that the contour * * * * * K * * * {\displaystyle \partial K} * is simple, that is, without self-intersections. Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below.

Rouche might refer to

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region
*
*
*
* K
*
*
* {\displaystyle K}
* with closed contour
*
*
*
*
* K
*
*
* {\displaystyle \partial K}
* , if |g(z)| < |f(z)| on
*
*
*
*
* K
*
*
* {\displaystyle \partial K}
* , then f and f + g have the same number of zeros inside
*
*
*
* K
*
*
* {\displaystyle K}
* , where each zero is counted as many times as its multiplicity. This theorem assumes that the contour
*
*
*
*
* K
*
*
* {\displaystyle \partial K}
* is simple, that is, without self-intersections. Rouché's theorem is an easy consequence of a stronger symmetric Rouché's theorem described below.

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