The generalised scaling function: A note

A method for determining the generalised scaling functions fn(g) arising in the high spin behaviour of long operator anomalous dimensions in the planar sl(2) sector of N=4 SYM is proposed. The all-order strong coupling expansion is detailed for the prototypical third and fourth scaling functions (f3(g), f4(g), respectively) and - together with high-precision numerical computations - reveals itself as crucial for disentangling the emergence of the O(6) Non-Linear Sigma Model mass-gap from different SYM 'mass' functions. Remarkably, only the fourth one gains contribution from the non-BES reducible densities and also shows up, as first, NLSM interaction and specific model dependence. Finally, the computation of the n-th generalised function is sketched and might be easily finalised for checks versus the computations in the sigma model or the complete string theory.