Calculation of the electromagnetic fields of dipole sources in plane-parallel layered media is an important problem of mathematical physics. Moreover, it is impossible to apply integral equation methods to analyze fields in media with inclusions without a sufficiently accurate and efficient method for solving such problems [1-5]. Desired solutions are usually constructed by means of the integral transformation method. They are expressed in terms of Fourier-Bessel integrals of the solutions to boundary value problems for ordinary differential equations with the spectral parameter. Solutions to these equations are found by recurrence formulas [1, 2, 4].
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