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We propose a regularization of the BFKL equation which allows for itssolution in each order of perturbation theory by means of a sum over multiplepoles. This sum can be presented in a rather simple formula for the Fouriertransform in the azimuthal angle of the gluon Green function. In order to testour method, we have compared a few orders in the expansion to previous resultsby Del Duca, Dixon, Duhr and Pennington, finding agreement. Our formalism isgeneral and can be applied to other, more complicated, kernels.

Order-by-order Analytic Solution to the BFKL Equation