Uniform asymptotic behavior of the diffraction field of a plane wave diffracted at a wedge with a finite edge

For the Dirichlet boundary condition, an expression is derived for the uniform asymptotic behavior of the diffraction field of a plane wave diffracted at the edge of a wedge. The expression takes into consideration the glancing incidence of one of the reflected waves on the edge. The first two terms of the asymptotic expansion of the field of an edge wave that is free of singularities at the light/shadow interface of a field reflected from an infinite edge are formulated.