Abstract
The paper proposes a method for calculating Sommerfeld integrals using the example of the problem of radiation from a Hertz dipole. An integral representation of the dipole field in the form of Sommerfeld integrals is given and its analytical expression is found in the form of an infinite power series. Qualitative and quantitative comparisons of the final results with exact expressions for the Hertz radiator obtained directly from integral representations in cylindrical and spherical coordinate systems are presented. The results of the paper may be used in the theory of diffraction and in solving the Sommerfeld problem