  Information about the neutron-star equation of state is encoded in the
waveform of a black hole-neutron star system through tidal interactions and the
possible tidal disruption of the neutron star. During the inspiral this
information depends on the tidal deformability Lambda of the neutron star, and
we find that Lambda is the best measured parameter during the merger and
ringdown as well. We performed 134 simulations where we systematically varied
the equation of state as well as the mass ratio, neutron star mass, and aligned
spin of the black hole. Using these simulations we have developed an analytic
representation of the full inspiral-merger-ringdown waveform calibrated to
these numerical waveforms, and we use this analytic waveform to estimate the
accuracy to which Lambda can be measured with gravitational-wave detectors. We
find that although the inspiral tidal signal is small, coherently combining
this signal with the merger-ringdown matter effect improves the measurability
of Lambda by a factor of ~3 over using just the merger-ringdown matter effect
alone. However, incorporating correlations between all the waveform parameters
then decreases the measurability of Lambda by a factor of ~3. The uncertainty
in Lambda increases with the mass ratio, but decreases as the black hole spin
increases. Overall, a single Advanced LIGO detector can measure Lambda for mass
ratios Q = 2--5, black hole spins J_BH/M_BH^2 = -0.5--0.75, neutron star masses
M_NS = 1.2M_sun--1.45M_sun, and an optimally oriented distance of 100Mpc to an
uncertainty of ~10%--100%. For the proposed Einstein Telescope, the uncertainty
in Lambda is an order of magnitude smaller.
