Examples
- All rational functions such as
-
- are meromorphic on the whole complex plane.
- The functions
-
- as well as the gamma function and the Riemann zeta function are meromorphic on the whole complex plane.
- The function
-
- is defined in the whole complex plane except for the origin, 0. However, 0 is not a pole of this function, rather an essential singularity. Thus, this function is not meromorphic in the whole complex plane. However, it is meromorphic (even holomorphic) on .
- The complex logarithm function
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- is not meromorphic on the whole complex plane, as it cannot be defined on the whole complex plane less an isolated set of points.
- The function
-
- is not meromorphic in the whole plane, since the point is an accumulation point of poles and is thus not an isolated singularity. The function
- is not meromorphic either, as it has an essential singularity at 0.
Read more about this topic: Meromorphic Function
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