SINGULARITIES AND ZEROS OF HOLOMORPHIC FUNCTIONS Contents

So far, our focus of study has been holomorphic functions. We will now concentrate on understanding points where functions are not holomorphic. In particular, we want to generalize our understanding of the behavior of f(z) = 1/z near z = 0 to a broader range of functions, and eventually prove interesting theorems about those functions. In particular, we will prove a generalization of Cauchy’s Theorem to functions which are more general than holomorphic functions.