  The solutions of an indeterminate Hamburger moment problem can be
parameterised using the Nevanlinna matrix of the problem. The entries of this
matrix are entire functions of minimal exponential type, and any growth less
than that can occur.
  An indeterminate moment problem can be considered as a canonical system in
limit circle case by rewriting the three-term recurrence of the problem to a
first order vector-valued recurrence. We give a bound for the growth of the
Nevanlinna matrix in terms of the parameters of this canonical system. In most
situations this bound can be evaluated explicitly. It is sharp in the sense
that for well-behaved parameters it coincides with the actual growth of the
Nevanlinna matrix up to multiplicative constants.
