Definition:Multiplicity
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Definition
Let $f : \C \to \C$ be a function.
Suppose there is $a \in \C$ such that $f(a) = 0$.
Then $a$ is said to be a zero of multiplicity $k$ if there exists non-zero $L \in \R$ such that:
- $\displaystyle \lim_{z \to a} \frac{|f(z)|}{|z-a|^k} = L$
Needs to be expanded so as to be relevant to other fields, not just $\C$.
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