Meromorphic Function - Examples

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
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.

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