A First Course in Complex Analysis · Problem 6.3.5

Power Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · harmonic-functions

Problem

Consider

u(x,y) = \ln\!\left(x^2 + y^2\right)

. (a) Show that

u

is harmonic on

\mathbb{C} \setminus \{0\}

. (b) Prove that

u

is not the real part of a function that is holomorphic in

\mathbb{C} \setminus \{0\}