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    Prove a meromorphic function is a rational function

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    1. Calculate residue for a complex function
    2. Prove a meromorphic function on an extended complex plane is a rational function

    If f has a pole of order M at p then:

    (see attached)

    using the above:

    compute the residues at each singularity in the complex plane C for the following function

    see attached

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    Solution Preview

    Question #1
    see attached

    Question #2
    Proof: Since f(z) is meromorphic on the extended complex plane, then it has only finite many poles, which can be assumed ...

    Solution Summary

    This solution helps calculate the residue for a complex function and prove a meromorphic function on an extended complex plane.