An old new class of meromorphic functions
  Based on the so-called re-scaling method, we will give a detailed description of the solutions to the Hamiltonian system (\ref{Hsystem}) below, which was discovered only recently by Kecker, and is strongly related to Painleve's fourth differential equation. In particular, the problem to determine those fourth Painleve transcendents with positive Nevanlinna deficiency $\delta(0,w)$, is completely resolved. 
Norbert Steinmetz
math.CV