  In the N=4 super Yang-Mills theory, we consider the higher order anomalous
dimensions gamma_L(g) of purely gluonic operators Tr(F^L) where F is a
component of the self-dual field strength. We propose compact closed
expressions depending parametrically on L that reproduce the prediction of
Bethe Ansatz equations up to five loop order, including transcendental dressing
corrections. The size dependence follows a simple pattern as the perturbative
order is increased and suggests hidden relations for these special operators.
