An accurate and efficient method for computing Sommerfeld type integrals is crucial in the analysis of the electromagnetic waves for radiators and scatters in the presence of a conducting half-space.In this paper

an analytical approach is described for the evaluation of the Hertz potential of a vertical magnetic dipole over the finitely conducting medium plane.By using the expansion of spherical wave functions for a cylindrical wave function and the techniques of the hypergeometric functions

the Sommerfeld integral contained in the potential is expressed as a rapidly and absolutely convergent series of spherical wave functions;and the coefficients of the series are cast into the Legender polynomials with complex argument for the medium parameter.The obtained result has the advantage that it holds without the restrictions on the locations of dipole source and observation points

ranges of medium parameters and frequency and so on

and can conveniently be employed to calculate and analyze the electromagnetic fields.