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Math Help - pole, removable, essential singularities

  1. #1
    GTO
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    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?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by GTO View Post
    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?
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  3. #3
    GTO
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    i think it is a composite function.
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