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Math Help - Entire functions and polynomials. Poles and singularities.

  1. #1
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    Entire functions and polynomials. Poles and singularities.

    Hi all ,
    please i need the solution of these question or at least Hints

    [1] Let f(z) be entire function and assume that there exist M, R >0 and n positive integer such that |f(z)|≤M(|z|^n) for all z in C-D(0,R). Prove that f(z) is a polynomial of degee≤n.

    [2] Suppose f and g have poles of order m and n respectively at z . Describe the singularity Of the following function at z :
    f+g, fg and f/g .
    Thanks all
    Last edited by mr fantastic; July 3rd 2010 at 06:13 AM. Reason: Re-titled.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by raed View Post
    Hi all ,
    please i need the solution of these question or at least Hints

    [1] Let f(z) be entire function and assume that there exist M, R >0 and n positive integer such that |f(z)|≤M(|z|^n) for all z in C-D(0,R). Prove that f(z) is a polynomial of degee≤n.

    [2] Suppose f and g have poles of order m and n respectively at z . Describe the singularity Of the following function at z :
    f+g, fg and f/g .
    Thanks all
    1.) See here

    2.) I suggest looking at the Laurent Series for f+g, fg, f/g
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  3. #3
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    Quote Originally Posted by chiph588@ View Post
    1.) See here

    2.) I suggest looking at the Laurent Series for f+g, fg, f/g
    Thank u very much
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