  We investigate the behaviour of the perturbative relation between the photon
energy spectrum in B -> Xs gamma and the hadronic P+ spectrum in semileptonic B
-> Xu l nu decay at high orders in perturbation theory in the "large-beta_0"
limit, in which only terms of order alpha_s^n beta_0^(n-1) are retained. The
leading renormalon in the weight function W(Delta,P_gamma) relating the two
spectra is confirmed to be at u=1/2, corresponding to nonperturbative
corrections at O(Lambda_QCD/m_b). We show that the P_gamma dependent pieces of
the weight function have no infrared renormalons in this limit, and so the
factorial growth in perturbation theory arises solely from the constant terms.
We find no numerical enhancement of leading logarithms, suggesting that
fixed-order perturbation theory is more appropriate than a leading-log
resummation for the extraction of |Vub|. The importance of various terms in the
expansion of the weight function is studied using a model for the B -> Xs gamma
photon spectrum. Our analysis suggests that higher order perturbative
corrections do not introduce a significant uncertainty in the extraction of
|Vub|.
