  We investigate the corrections to scaling of the Renyi entropies of a region
of size l at the end of a semi-infinite one-dimensional system described by a
conformal field theory when the corrections come from irrelevant boundary
operators. The corrections from irrelevant bulk operators with scaling
dimension x have been studied by Cardy and Calabrese (2010), and they found not
only the expected corrections of the form l^(4-2x) but also unusual corrections
that could not have been anticipated by finite-size scaling arguments alone.
However, for the case of perturbations from irrelevant boundary operators we
find that the only corrections that can occur to leading order are of the form
l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1)
when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally
irrelevant boundary perturbation will give leading corrections going as
log(l)^(-3). No unusual corrections occur when perturbing with a boundary
operator.
