A simple pole is a type of singularity of a meromorphic function where the function approaches infinity in a linear manner. This means that at a simple pole, the function can be expressed in the form $$f(z) = \frac{g(z)}{(z - z_0)}$$, where $$g(z)$$ is analytic and non-zero at the point $$z_0$$. Understanding simple poles is crucial as they play a significant role in determining the behavior of meromorphic functions and their residues.
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