  We adapt and modify the eigenfunction method of computing the power-law
spectrum of particles accelerated at a relativistic shock front via the
first-order Fermi process (Kirk, J.G., Schneider, P., Astrophysical Journal
315, 425 (1987)) to apply to shocks of arbitrarily high Lorentz factor. The
power-law index of accelerated particles undergoing isotropic small-angle
scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23
+/- 0.2 (where s=d\ln f/ d\ln p, with f the Lorentz-invariant phase-space
density and p the momentum), in agreement with the results of Monte-Carlo
simulations. We present results for shocks in plasmas with different equations
of state and for Lorentz factors ranging from 5 to infinity.
