Deriving accurate peculiar velocities (even at high redshift)

The way that peculiar velocities are often inferred from measurements of distances and redshifts makes an approximation, v_p = cz-H_0 D, that gives significant errors even at relatively low redshifts (overestimates peculiar velocity by ~ 100 km/s at z~0.04). Here we demonstrate where the approximation breaks down, the systematic offset it introduces, and how the exact calculation should be implemented.