  We give an alternative and simpler method for getting pointwise estimate of
meromorphic solutions of homogeneous linear differential equations with
coefficients meromorphic in a finite disk or in the open plane originally
obtained by Hayman and the author. In particular, our estimates generally give
better upper bounds for higher order derivatives of the meromorphic solutions
under consideration, are valid, however, outside an exceptional set of finite
logarithmic density.
  The estimates again show that the growth of meromorphic solutions with a
positive deficiency at infinity can be estimated in terms of initial conditions
of the solution at or near the origin and the characteristic functions of the
coefficients.

Complex Variables