  We describe a procedure for determining the generalised scaling functions
$f_n(g)$ at all the values of the coupling constant. These functions describe
the high spin contribution to the anomalous dimension of large twist operators
(in the $sl(2)$ sector) of ${\cal N}=4$ SYM. At fixed $n$, $f_n(g)$ can be
obtained by solving a linear integral equation (or, equivalently, a linear
system with an infinite number of equations), whose inhomogeneous term only
depends on the solutions at smaller $n$. In other words, the solution can be
written in a recursive form and then explicitly worked out in the strong
coupling regime. In this regime, we also emphasise the peculiar convergence of
different quantities ('masses', related to the $f_n(g)$) to the unique mass gap
of the $O(6)$ nonlinear sigma model and analyse the first next-to-leading order
corrections.
