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We propose a scheme for determining a generalised scaling function, namelythe Sudakov factor in a peculiar double scaling limit for high spin and largetwist operators belonging to the $sl(2)$ sector of planar ${\cal N}=4$ SYM. Inparticular, we perform explicitly the all-order computation at strong 't Hooftcoupling regarding the first (contribution to the) generalised scalingfunction. Moreover, we compare our asymptotic results with the numericalsolutions finding a very good agreement and evaluate numerically thenon-asymptotic contributions. Eventually, we illustrate the agreement andprediction on the string side.

Strong coupling for planar ${\cal N}=4$ SYM theory: an all-order result