1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

268 CHAPTER 7 • TAYLOR AND LAURENT SERIES

Definition 7 .4: Annulus

Given 0 Sr < R, we define the annulus centered at O' with radii r and R by

A(a,r, R) = {z: r < lz - a:I < R}.

The closed annulus centered at o: with radii r and R is denoted by

A (o:, r , R ) = {z : r S lz -a l S R}.

Figure 7.3 illustrates these terms.

y

Figure 7.3 The closed annulus A (a, r, R ). The shaded portion is t he open annulus

A(Ck,r,R).