Plot of the absolute value of the gamma function, showing several poles.

The pole of a meromorphic complex function is a point on the complex plane on which the function is undefined, or approaches infinity. Any rational complex function will have poles where the denominator is equal to zero. A function

$ f(z) = \frac{g(z)}{(z-p)^n} $

will have a pole of order n when z=p. If n = 1, the point is called a simple pole. If n = 0, the point is a removable singularity (that is, the limit exists).

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