  We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills
theory at strong coupling which correspond to minimal surfaces with a
light-like polygonal boundary in AdS_3. We find a concise expression of the
remainder function in terms of the T-function of the associated thermodynamic
Bethe ansatz (TBA) system. Continuing our previous work on the analytic
expansion around the CFT/regular-polygonal limit, we derive a formula of the
leading-order expansion for the general 2n-point remainder function. The
T-system allows us to encode its momentum dependence in only one function of
the TBA mass parameters, which is obtained by conformal perturbation theory. We
compute its explicit form in the single mass cases. We also find that the
rescaled remainder functions at strong coupling and at two loops are close to
each other, and their ratio at the leading order approaches a constant near 0.9
for large n.
