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In this paper, we derive the Ewald method for inverse power-law interactionsin quasi-two dimensional systems. The derivation is done by using two differentanalytical methods. The first uses the Parry's limit, that considers the Ewaldmethods for quasi-two dimensional systems as a limit of the Ewald methods fortridimensional systems, the second uses Poisson-Jacobi identities for latticesums. Taking into account the equivalence of both derivations, we obtain a newanalytical Fourier transform intregral involving incomplete gamma function.Energies of the generalized restrictive primitive model of electrolytes($\eta$-RPM) and of the generalized one component plasma model ($\eta$-OCP) aregiven for the tridimensional, quasi-two dimensional and monolayers systems. Fewnumerical results, using Monte-Carlo simulations, for $\eta$-RPM and $\eta$-OCPmonolayers systems are reported.

Ewald methods for inverse power-law interactions in tridimensional and quasi-two dimensional systems