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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. Furthermore, they are the only meromorphic functions on the [[riemann sphere|extended 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/>
* 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>.
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