  The classical Dirichlet problem for a second-order strongly elliptic system
with constant coefficients in a Jordan domain is considered. We show that the
solution of the problem can be represented as a functional series in powers of
the parameter, which determines the deviation of the system operator from the
Laplacian. This series converges uniformly in the closure of the region under
the assumption that the boundary of the region and the boundary function
satisfy the sufficient regularity conditions: the trace of a conformal mapping
of the domain onto a circle composed with the boundary function belongs to the
Holder class with exponent greater than 1/2.
