Teorema de Picard

Abstract

In this work, we study Picrad’s theorems about the range of an analytic function. The first approach to Picard Theorem is the Casorati-Weierstrass Theorem which ensures that the range of an analytic function near an essential singularity is dense in C. In Chapter 3, we prove Little Picard Theorem: if a function f is entire and non constant, the set of values that f assumes is either the whole complex plane or the plane minus a single point. In Chapter 4, we prove Great Picard Theorem: if an analytic function f has an essential singularity at a point z0 then at any punctured neighborhood of z0, f(z) attains every finite complex value with at most one possible exception.