[en] We derive an expression for the effective mass of an electron for a multi-band system, starting from a thermodynamic potential expressed in terms of a single-particle Green’s function and using an effective equation of motion in the effective mass representation (EMR). We consider a four-band model around $\mathrm{\Gamma <!--\; ??\; -->}$ point-one conduction band and three valence bands, for the w-ZnO. We diagonalize the $\stackrel{\to <!--\; ???\; -->}{k}\cdot <!--\; ???\; -->\stackrel{\to <!--\; ???\; -->}{\mathrm{\pi <!--\; ??\; -->}}$ Hamiltonian, using double-group basis functions for the energy levels, by considering the conduction band and each of the valence bands separately, and obtain the energy dispersions in terms of Luttinger–Kohn parameters. Effects of other bands on each of the valence band energy is considered by going beyond parabolic approximation and adding fourth degree terms in the wave vector to the energy dispersion. The resulting bands’ structures agree well with other reported electronic structures. The formalism is then used to calculate the effective masses and effective g-factors at the $\mathrm{\Gamma <!--\; ??\; -->}$ point, and as functions of the wave vector. Comparisons with other calculated values and experimental values show reasonably good agreement. (paper)