  Several new families of exact solution to the Einstein-Maxwell system of
differential equations are found for anisotropic charged matter. The spacetime
geometry is that of Finch and Skea which satisfies all criteria for physical
acceptability. The exact solutions can be expressed in terms of elementary
functions, Bessel functions and modified Bessel functions. When a parameter is
restricted to be an integer then the special functions reduce to simple
elementary functions. The uncharged model of Finch and Skea (Class. Quantum
Grav. 6, 467 (1989)) and the charged model of Hansraj and Maharaj (Int. J. Mod.
Phys. D 8, 1311 (2006)) are regained as special cases. The solutions found
admit a barotropic equation of state. A graphical analysis indicates that the
matter and electric quantities are well behaved.
