# Math Help - pole, removable, essential singularities

1. ## pole, removable, essential singularities

Let $f: D(P,r)$\ $\{P\} \rightarrow C$ be holomorphic. Let $U=f(D(P,r)$\ $\{P\})$. Assume that $U$ is open. Let $g:U \rightarrow C$ be holomorphic. If $f$ has a removable singularity at $P$, does $p \circ f$ have one also? what about the case of poles and essential singularities?

2. Originally Posted by GTO
Let $f: D(P,r)$\ $\{P\} \rightarrow C$ be holomorphic. Let $U=f(D(P,r)$\ $\{P\})$. Assume that $U$ is open. Let $g:U \rightarrow C$ be holomorphic. If $f$ has a removable singularity at $P$, does $p \circ f$ have one also? what about the case of poles and essential singularities?
Do you mean $g\circ f$?

3. i think it is a composite function.