Abstract: We consider the approximation of a special class of complex functions f that is analytic on the disk \textU = \left\ z \in \rmC:\dfrac12 < \left| z \right| < 1 \right\ , whose origin is its essential singularity. We obtain the exact Jackson inequality between the best approximation E_n - 1\left( f \right)_2 of functions f and m-order continuous modules of functions z^rf^\left( r \right) . We also obtain the exact Jackson inequality between the best approximation E_n - 1\left( f \right)_2 of function f and \calK -functional. Then we obtain the exact Jackson inequality between the best approximation E_n - 1\left( f \right)_2 of functions f and weighted integral of m-order continuous modules of functions z^rf^\left( r \right) . Finally, we obtain the best approximation and n-widths in the functions classes of m-order continuous modules of functions z^rf^\left( r \right) , in the functions classes of weighted integral of m-order continuous modules of functions z^rf^\left( r \right) and in the functions classes of \calK -functional respectively.