Complex Analysis: Theory and Applications · Problem 6.6.6

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · liouville-theorem

Problem

Let

f

be an entire function such that

|f(z)| \leq M|z|

for all

z

. ((a)) Show that, for

n \geq 2

f^{(n)}(z) = 0

for all

z

. ((b)) Use part (a) to show that

f(z) = az + b