We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green’s function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.