We propose a regularization of the BFKL equation which allows for its
solution in each order of perturbation theory by means of a sum over multiple
poles. This sum can be presented in a rather simple formula for the Fourier
transform in the azimuthal angle of the gluon Green function. In order to test
our method, we have compared a few orders in the expansion to previous results
by Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism is
general and can be applied to other, more complicated, kernels.Comment: 23 pages, 1 figur
