On the behaviour of the successive derivatives of meromorphic functions on the final set

We study the behaviour of the sequence of successive derivatives of
meromorphic functions at points of the so-called final set. We prove that, whereas
in many cases this sequence tends to ∞, for a special class of meromorphic functions,
it may have extremely wild behaviour. We also prove a connection between
the derivatives of meromorphic functions from this class and so-called Dirichlet
sets.