Diffraction coefficients for a circular impedance cone

The axially symmetric problem of scattering of an incident plane wave by a circular cone with an impedance boundary condition on its face is considered. The scheme of solution includes applying the Kontorovich-Lebedev transform, derivation of a second-order difference equation in a strip of a complex variable and its reduction to an integral equation of the convolution type with variable coefficients. An approximate solution by a collocation method is constructed. The diffraction coefficients are found in terms of the solution of the integral equation. Numerical results for the diffraction coefficients are reported.