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We compute the fully-differential B -> X_u l nu decay width to all orders inperturbation theory in the large-beta0 limit. Each of the five structurefunctions that build the hadronic tensor is expressed as a Borel integral,summing up O(CF beta0^{n-1} alpha_s^n) corrections for any n. We deriveanalytic expressions for the Borel transforms of both real and virtual diagramswith a single dressed gluon, and perform an all-order infrared subtraction,where the Borel parameter serves also as an infrared regulator. Expanding theresult we recover the known triple-differential NLO coefficient, and obtain anexplicit expression for the O(CF beta0 alpha_s^2) triple-differential NNLOcorrection. This result can be used to improve the determination of |V_{ub}|from inclusive B -> X_u l nu measurements at the B factories with a variety ofkinematic cuts.Comment: 40 page

Running-coupling effects in the triple-differential charmless semileptonic decay width