A First Course in Complex Analysis · Problem 6.3.4

Power Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Let

u(x,y) = e^x \sin y

. (a) Show that

u

is harmonic on

\mathbb{C}

. (b) Find an entire function

f

such that

\operatorname{Re}(f) = u