Asymptotic expansion of the Dirichlet problem with Laplace equation outside a thin disk

A uniform asymptotic expansion is found for the exterior Dirichlet problem with Laplace equation outside a thin disk in three-dimensional space. The small parameter is the thickness of the disk. The asymptotic coefficients are constructed by means of the matching method up to solutions of boundary value problems. Near the edges of the disk, the coefficients are presented as series of special functions without specifying the explicit form of the coefficients at the functions. However, it is proved that there exist some coefficients independent of the small parameter.