Diffraction of electromagnetic waves by a partially screened dielectric anisotropic cylinder (Q2754731)

Mathematically, the considered problem is reduced to dual series equations in trigonometric functions. The convenient technique of reducing these equations to infinite algebraic systems is inapplicable due to slow convergence. An alternative method of solution of the equations, that uses analytical regularization with the aid of the Riemann-Hilbert conjugation problem, is suggested. Thus the system of dual series equations is reduced to reconstruction of some function, analytical outside an arc, by its values on this arc. At the end, an infinite system of algebraic equations is obtained. It is shown, that a solution of this system exists, is unique and can be computed by the reduction technique.