We used the generalized form of the Thomas--Fermi type for the density profile inside spherical nuclei to obtain a leptodermous expansion for the matter density. This expansion was used to calculate the energy coefficients of the liquid drop model formula. We obtained analytical expressions for the volume, surface, curvature and higher order energy coefficients. These analytical expressions were used to derive a liquid drop model expansion for compressibility of spherical nuclei. We studied the energy and compressibility expansion coefficients and also their convergence. Particular interest was focused on the study of surface and curvature properties.

PACS numbers: 21.10.Dr, 21.60.Jz