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On the SaddlePoint Method of Integration
Expansions Valid in the Vicinity of the Interface
5 other sections not shown
accordance with Eq asymptotic range asymptotic series boundary conditions bracket branch cut branch points Chapter comparison with unity conducting medium conformal transformation contour C1 corresponding cos0 cosw defined by Eq dipole embedded double integral electromagnetic field components evaluation expansion coefficients exponent exponential factor fundamental integrals given by Eq Green's function Hankel function Helmholtz equation Hertzian dipole horizontal electric dipole horizontal magnetic dipole integral representations integrand interface leading term low frequency manner we obtain neglecting terms observation close observation in air observation in medium original path path C2 path of integration path of steepest points of observation power flow power series expansion Poynting's vector quasi-static radius of convergence real axis reciprocal powers Riemann surface saddle-point method Sheet Sommerfeld denominator source dipole steepest descents surface wave type Hertz vectors variable of integration vertical axis vertical electric dipole vertical magnetic dipole vicinity Watson's lemma