  In this article we are interested in finding positive discrete harmonic
functions with Dirichlet conditions in three quadrants. Whereas planar lattice
(random) walks in the quadrant have been well studied, the case of walks
avoiding a quadrant has been developed lately. We extend the method in the
quarter plane -- resolution of a functional equation via boundary value problem
using a conformal mapping -- to the three-quarter plane applying the strategy
of splitting the domain into two symmetric convex cones. We obtain a simple
explicit expression for the algebraic generating function of harmonic functions
associated to random walks avoiding a quadrant.
