Examples of meromorphic functions are all rational functions such as *f*(*z*) = (*z*^{3}-2*z* + 1)/(*z*^{5}+3*z*-1), the functions *f*(*z*) = exp(*z*)/*z* and *f*(*z*) = sin(*z*)/(*z*-1)^{2} as well as the Gamma function and the Riemann zeta function. The functions *f*(*z*) = ln(*z*) and *f*(*z*) = exp(1/*z*) are not meromorphic.

In the language of Riemann surfaces, a meromorphic function is the same as a holomorphic function from the complex plane to the Riemann sphere which is not constant ∞. The poles correspond to those complex numbers which are mapped to ∞.