A new transform method for investigating boundary value problems for partial differential equations was introduced by Fokas in the late 1990s. In this paper, we implement this approach to a mixed boundary value problem for the Helmholtz equation in a convex wedge. The solution in the form of integral representation is derived, and the generalized Dirichlet to Neumann map is studied.

Fokas transform method, Helmholtz equation, boundary value problem, Riemann-Hilbert technique, Dirichlet to Neumann map.