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We say f is meromorphic, then f is defined on U except at discrete set of points S which are poles. If [itex]z_0[/itex] is such a point, then there exist m in integers such that [itex](z-z_0)^mf(z)[/itex] is holomorphic in a neighborhood of [itex]z_0[/itex].

A pole is [itex]\lim_{z\to a}|f(z)| =\infty[/itex].

S0 the trouble is showing that f is the quotient of two holomorphic functions.