Complex Analysis: Theory and Applications · Problem 3.1.3

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · entire-functions

Problem

f

and

g

are entire functions, which of the following are necessarily entire? (a)

[f(z)]^3

. (b)

f(z)g(z)

. (c)

\dfrac{f(z)}{g(z)}

. (d)

f\!\left(\dfrac{1}{z}\right)

. (e)

f(z-1)

. (f)

f\!\left(g(z)\right)