1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

288 CHAPTER 7 • TAYLOR AND LAURENT SERIES

II Corollary 7.12 If f is analytic in D; (a), then f can be defined to be analytic
at a iff lim f (z) exists and is finite. •
...... "'

•EXAMPLE 7 .16 Show that the function g defined by

{

• :It
  g(z)= ~,
  when z f= 0, and

when z = 0,

is not continuous at z = O.

Solution In Exercise 20, Section 7.2, we asked you to show this relation by

computing limits along t he real and imaginary axes. Note, however, that the