Boundary integrodifferential equations for electromagnetic scattering problems in three dimensions

On the basis of two vector representations of electromagnetic fields we introduce a new system of boundary integrodifferential equations for the solution of scattering problems in three dimensions. The unknowns of this system present two scalar functions, namely, the "null" coefficients of Atkinson-Wilcox expansion; electromagnetic field being reconstructed with these functions by means of certain recursive-differential operators. We define an algebraic analog of the equations by expanding unknowns into Fourier series with respect to spherical harmonics. Verification of the approach is done on the basis of the solution of well-known canonical problems