New formulas for the electromagnetic field of a vertical electric dipole in a dielectric or conducting half-space near its horizontal interface

New formulas are derived for the electromagnetic field of a vertical electric dipole in a conducting or dielectric half-space. These continuously approximate in accuracy the general complex integrals over the entire practical range, yet are quite simple. They supplement similar formulas for the horizontal electric dipole with which they are compared, and provide the means for studying the interference patterns between the direct and lateral components of the waves and the reflection and transmission of lateral waves at boundaries.