# Prove a meromorphic function is a rational function

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.

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