We consider the problem of solving the three-dimensional scalar Helmholtz equation in the exterior of a circular disk under the assumption that on the disk radially symmetric Dirichlet data are prescribed. Physical processes leading to this problem are, for example, the diffraction of a wave (acoustic) by a circular aperture in a rigid infinite plane screen and the diffusion through a circular hole. We construct two sequences of functions, defined on the disk, which together form a biorthogonal system. We show that these functions as well as the inverse image functions, with respect to the boundary integral equation of the considered problem, of the functions of the first sequence can be expressed explicitly. Thus, if arbitrary Dirichlet data on the disk are expanded into the functions of the first sequence, the solution of the governing boundary integral equation is given by a closed-form series representation. In [N. Gorenflo, A new explicit solution method for the diffraction through a slit – part 2, Z. Angew. Math. Phys. 58 (2007), pp. 16–36] the same results have been obtained for the problem of the diffraction by a slit.