A First Course in Complex Analysis · Problem 7.5.22

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · pointwise-uniform-convergence

Problem

Where do the following sequences converge pointwise? Do they converge uniformly on this domain? (a)

(n z^n)

(b)

\left(\dfrac{z^n}{n}\right)

(c)

\left(\dfrac{1}{1+nz}\right)

where

\operatorname{Re}(z) \geq 0