The explicit solution of the equation Δu=f in a plane infinite angle, satisfying on one side of the angle a Neumann condition and on the other one the condition ∂u/∂n + h∂u/∂r + σu=Ψ (∂/∂r is the tangential derivative, σ ε C, ℜσ ≥ 0), is constructed and estimated in weighted Sobolev spaces. The obtained estimates are sharp with respect to the differential order and are uniform with respect to σ. The construction of the solution reduces to the investigation of a finite difference equation in the complex plane, arising after a Mellin transform. © 1992 Plenum Publishing Corporation.