Examples of meromorphic functions are all rational functions such as f(z) = (z^{3}2z + 1)/(z^{5}+3z1), the functions f(z) = exp(z)/z and f(z) = sin(z)/(z1)^{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 ∞.
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