  Recently, Freyhult, Rej and Staudacher (FRS) proposed an integral equation
determining the leading logarithmic term of the anomalous dimension of sl(2)
twist-operators in N=4 SYM for large Lorentz spin M and twist L at fixed j =
L/log(M). We discuss the large j limit of the FRS equation. This limit can be
matched with the {\em fast long string} limit of AdS_5 X S^5 superstring
perturbation theory at all couplings. In particular, a certain part of the
classical and one-loop string result is known to be protected and can be
computed in the weakly coupled large-j limit of the FRS equation. We present
various analytical and numerical results supporting agreement at one and two
loops in the gauge theory.
