New classes of exact solutions of the Einstein field equation are found in closed form for a static spherically symmetric anisotropic star by generalizing earlier approaches. The field equations are integrated by specifying one of the gravitational potentials and the anisotropic factor which are physically reasonable. We demonstrate that it is possible to obtain a more general class of solutions to the Einstein field equation in the form of series with anisotropic matter. For specific parameter values it is possible to find new exact models for the Einstein system in terms of elementary functions from the general series solution.
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