The finite range Wiener-Hopf integral equation and a boundary value problem in a waveguide

In this paper the boundary value problem of a finite bifurcation in a rectangular waveguide is formulated in terms of a finite range Wiener-Hopf integral equation, and the solution of the integral equation is presented. As a first step, an infinite set of simultaneous equations is obtained from the integral equation. The solution of the above set of equations is then obtained by analytic means. It is indicated that the method developed can be applied to certain other problems of mathematical physics and a number of examples of such problems are included.