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We calculate the two-loop QCD correction to the form factors of on-shellb-quark decay to an energetic massless quark, which constitutes the lastmissing piece required for an O(alpha_s^2) determination of |V_ub| frominclusive semi-leptonic \bar B --> X_u l nu decays in the shape-functionregion.

Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region