We have compared the lateral analytical structure functions coming from cascade theory to the numerical distributions generated by EAS Monte Carlo simulations and to the empirical functions used in giant air showers experiments.
Introducing the Gaussian hypergeometric formalism, we have improved the analytical description in the most common topological situations and we propose a new function characterized by both terms fitted separately to the electron-positron and the muon components. Important effects in the accuracy of the core position determination
are underlined and consequences for the primary energy estimation are discussed. The consecutive treatment and interpretation of the data contained in the catalogues of Volcano Ranch and Yakutsk, completed by the most energetic event of AGASA, are presented. Results might have important implications for detector configuration of the future giant air shower arrays
