If f is meromorphic on U with only a finite number of poles, then [itex]f=\frac{g}{h}[/itex] where g and h are analytic on U.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# If f is meromorphic on U with only a finite number of poles, then

**Physics Forums | Science Articles, Homework Help, Discussion**