  Starting from the known all-order expressions for the BFKL eigenvalue and
impact factor, we establish a formalism allowing the direct calculation of the
six-point remainder function in N=4 super-Yang-Mills theory in momentum space
to - in principle - all orders in perturbation theory. Based upon identities
which relate different integrals contributing to the inverse Fourier-Mellin
transform recursively, the formalism allows to easily access the full remainder
function in multi-Regge kinematics up to 7 loops and up to 10 loops in the
fourth logarithmic order. Using the formalism, we prove the all-loop formula
for the leading logarithmic approximation proposed by Pennington and
investigate the behavior of several newly calculated functions.
