  In recent works [hep-th/9909147, hep-th/0005259] was found a wonderful
correlation between integrable systems and meromorphic functions. They reduce a
problem of effictivisation of Riemann theorem about conformal maps to
calculation of a string solution of dispersionless limit of the 2D Toda
hierarchy. In [math.CV/0103136] was found a recurrent formulas for coeffciens
of Taylor series of the string solution. This gives, in particular, a method
for calculation of the univalent conformal map from the until disk to an
arbitrary domain, described by its harmonic moments.
  In the present paper we investigate some properties of these formulas. In
particular, we find a sufficient condition for convergence of the Taylor series
for the string solution of dispersionless limit of 2D Toda hierarchy.
