Suppose that f(z) = u(x , y) + i*v(x, y) (where z = x + i*y) is ENTIRE and not constant. Use Liouville's theorem to prove that v(x, y) is unbounded. Under what conditions can a function that is harmonic everywhere be bounded?© BrainMass Inc. brainmass.com October 10, 2019, 12:10 am ad1c9bdddf
Let . Since is entire, then is also entire.
I claim that is unbounded.
If is bounded, ...
Liouville's theorem is applied.