Meromorphic function
A meromorphic function isfunction thatholomorphic almost everywhere oncomplex plane, except forsetisolated poless, whichcertain well-behaved singularities. Every meromorphic function can be expressed asratio between two entire functions (withdenominator not constant 0):poles then occur atzeroes ofdenominator.Examplesmeromorphic functionsall rational functions such as f(z) = (z3-2z + 1)/(z5+3z-1),functions f(z) = exp(z)/zf(z) = sin(z)/(z-1)2 as well asGamma function andRiemann zeta function. The functions f(z) = ln(z)f(z) = exp(1/z)not meromorphic.
InlanguageRiemann surfaces,meromorphic function issame asholomorphic function fromcomplex plane toRiemann sphere whichnot constant ∞. The poles correspondthose complex numbers whichmapped∞.
