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==Examples==
* All [[rational function]]s,<ref name=Lang_1999>{{cite book |last=Lang |first=Serge |author-link=Serge Lang |year=1999 |title=Complex analysis |publisher=[[Springer-Verlag]] |___location=Berlin; New York |edition=4th |isbn=978-0-387-98592-3}}</ref> for example <math display="block"> f(z) = \frac{z^3 - 2z + 10}{z^5 + 3z - 1}, </math> are meromorphic on the whole complex plane.
:* The functions <math display="block"> f(z) = \frac{e^z}{z} \quad\text{and}\quad f(z) = \frac{\sin{z}}{(z-1)^2} </math> as well as the [[gamma function]] and the [[Riemann zeta function]] are meromorphic on the whole complex plane.<ref name=Lang_1999/> ▼::<math> f(z) = \frac{z^3 - 2z + 10}{z^5 + 3z - 1}, </math>
:* The function <math display="block"> f(z) = e^\frac{1}{z} </math> 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 <math>\mathbb{C} \setminus \{0\}</math>. ▼:are meromorphic on the whole complex plane.
:* The [[complex logarithm]] function <math display="block"> f(z) = \ln(z) </math> is not meromorphic on the whole complex plane, as it cannot be defined on the whole complex plane while only excluding a set of isolated points.<ref name=Lang_1999/> ▼* The functions
:* The function <math display="block"> f(z) = \csc\frac{1}{z} = \frac1{\sin\left(\frac{1}{z}\right)} </math> is not meromorphic in the whole plane, since the point <math>z = 0</math> is an [[Limit point|accumulation point]] of poles and is thus not an isolated singularity.<ref name=Lang_1999/> ▼::<math> f(z) = \frac{e^z}{z} \quad\text{and}\quad f(z) = \frac{\sin{z}}{(z-1)^2} </math>
:* The function <math display="block"> f(z) = \sin \frac 1 z </math> is not meromorphic either, as it has an essential singularity at 0. ▼▲:as well as the [[gamma function]] and the [[Riemann zeta function]] are meromorphic on the whole complex plane.<ref name=Lang_1999/>
* The function
::<math> f(z) = e^\frac{1}{z} </math>
▲: 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 <math>\mathbb{C} \setminus \{0\}</math>.
* The [[complex logarithm]] function
::<math> f(z) = \ln(z) </math>
▲:is not meromorphic on the whole complex plane, as it cannot be defined on the whole complex plane while only excluding a set of isolated points.<ref name=Lang_1999/>
* The function
::<math> f(z) = \csc\frac{1}{z} = \frac1{\sin\left(\frac{1}{z}\right)} </math>
▲:is not meromorphic in the whole plane, since the point <math>z = 0</math> is an [[Limit point|accumulation point]] of poles and is thus not an isolated singularity.<ref name=Lang_1999/>
* The function
::<math> f(z) = \sin\frac1z </math>
▲:is not meromorphic either, as it has an essential singularity at 0.
==On Riemann surfaces==
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