Complex Analysis: Theory and Applications · Problem 6.6.5

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · cauchy-inequalities

Problem

Let

f

be analytic in the disk

D_5(0)

and suppose that

|f(z)| \leq 10

for

z \in C_3(1)

. ((a)) Find a bound for

|f^{(4)}(1)|

. ((b)) Find a bound for

|f^{(4)}(0)|

. Hint:

\overline{D}_2(0) \subseteq \overline{D}_3(1)

. Use Theorems 6.16 and 6.17.