  We investigate the Eden-Staudacher equation for the anomalous dimension of
the twist-2 operators at the large spin s in the N=4 super-symmetric gauge
theory. This equation is reduced to a set of linear algebraic equations with
the kernel calculated analytically. We prove that in perturbation theory the
anomalous dimension is a sum of products of the Euler functions zeta(k) having
the property of the maximal transcendentality with the coefficients being
integer numbers. The radius of convergency of the perturbation theory is found.
It is shown, that at g=infty the kernel has an essential singularity. The
analytic properties of the solution of the Eden-Staudacher equation are
investigated. In particular for the case of the strong coupling constant the
solution has an essential singularity on the second sheet of the variable j
appearing in its Laplace transformation. Similar results are derived also for
the Beisert-Eden-Staudacher equation which includes the contribution from the
phase related to the crossing symmetry of the underlying S-matrix. We show,
that its singular solution at large coupling constants reproduces the anomalous
dimension predicted from the string side of the AdS/CFT correspondence.
