1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

7.3 • LAURENT SERIES REPRESENTATIONS 269

The main result of this section specifies how functions analytic in an annulus
can be expanded in a Laurent series. In it, we use symbols of the form Ct (a),
which- we remind you-designate the positively oriented circle with radius p

and center a. That is, Ct (a)= {z: lz -al= p}, oriented counterclockwise.

y

Figure 7.4 The annulus A (shaded) and, in its interior, the circles Go, Ci, and G2.