Abstract
This chapter discusses the applications of the Cauchy theory. A nonconstant analytic function maps open sets onto open sets, and a one-to-one analytic function has an analytic inverse. One must first obtain some information about the number of solutions of the equation f(z) = w, where w is fixed and z ranges over a neighborhood of a zero of f. The chapter also discusses the behavior of an analytic function that maps one disk into another. The linear fractional transformations are of this type. It will be convenient to have a version of Cauchy's theorem and integral formula for functions that are analytic in a region bounded by a closed path and continuous on the closure of the region. The basic tool is the Poisson integral formula, which may be regarded as an analog of the Cauchy integral formula for real valued functions.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
