  The aim of this work is to generalize the ultraholomorphic extension theorems
from V. Thilliez in the weight sequence setting and from the authors in the
weight function setting (of Roumieu type) to a mixed framework. Such mixed
results have already been known for ultradifferentiable classes and it seems
natural that they have ultraholomorphic counterparts. In order to have control
on the opening of the sectors in the Riemann surface of the logarithm for which
the extension theorems are valid we are introducing new mixed growth indices
which are generalizing the known ones for weight sequences and functions. As it
turns out, for the validity of mixed extension results the so-called order of
quasianalyticity (introduced by the second author for weight sequences) is
becoming important.
