Level sets of potential functions bisecting unbounded quadrilaterals

We study the mixed Dirichlet–Neumann problem for Laplace equation in complement of a bounded convex polygonal quadrilateral extended complex plane. The Dirichlet / Neumann conditions at opposite pairs sides are $$\{0,1\}$$ and $$\{0,0\},$$ resp. solution to this is harmonic function unbounded polygon known as potential quadrilateral. compute values u including its value infinity. main result paper Theorem 4.3 which yields formula $$u(\infty )$$ expressed terms angles given well-known special functions. use two independent numerical methods illustrate our result. first method Mathematica program second one based on using MATLAB toolbox PlgCirMap. case quadrilateral, exterior unit disc with four fixed points boundary, considered well.