1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

148 CHAPTER 4 • SEQUENCES, JULIA AND MANDELBROT SETS, AND POWER SERIES

Another way to phrase case (ii) of Theorem 4.15 is to say that the power

00

series f (z) = L: Cn (z -a)" converges if lz -al < p and diverges if lz - a l > p.

n=O
We call the number p the radius of convergence of the power series (see Figure
4.3). For case ( i) of Theorem 4.14, we say that the radius of convergence is zero
and that the radius of convergence is infinity for case (iii).