Asymptotics of the solution of the Dirichlet problem for the Laplace and Helmholtz equations in the exterior of a slender cylinder

The Dirichlet problem is investigated for the Laplace and Helmholtz equations in the exterior of a surface in $\mathbf R^3$ which is a right circular cylinder outside a sphere. Asymptotic expansions of the solutions are constructed; the small parameter is the maximal diameter of the cross-section of the cylinder.
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