A meromorphic function is a single-valued function that is analytic in all but possibly a discrete subset of its domain, and at those singularities it must go to infinity like a polynomial (i.e., these exceptional points must be poles and not essential singularities). A simpler definition states that a meromorphic function is a function f(z) of the form f(z) = (g(z))/(h(z)) where g(z) and h(z) are entire functions with h(z)!=0.

analytic function | entire function | essential singularity | holomorphic function | pole | real analytic function | Riemann sphere