  We propose a scheme for determining a generalised scaling function, namely
the Sudakov factor in a peculiar double scaling limit for high spin and large
twist operators belonging to the $sl(2)$ sector of planar ${\cal N}=4$ SYM. In
particular, we perform explicitly the all-order computation at strong 't Hooft
coupling regarding the first (contribution to the) generalised scaling
function. Moreover, we compare our asymptotic results with the numerical
solutions finding a very good agreement and evaluate numerically the
non-asymptotic contributions. Eventually, we illustrate the agreement and
prediction on the string side.
