RASCAS simulations of the transfer of Lyman-α photons (x_in = 0) emitted at the origin of a uniform plane-parallel slab with τ_H I = 10⁷ and T = 10 K. Top: relative difference between the emerging spectra computed with the approximation from Tasitsiomi (2006) and that computed with the approximation from Humlíček (1982). Bottom: as in the top panel, but in units of the Poisson error (i.e. the variance due to the limited number of photons per bin in frequency; σ). The horizontal dashed lines show ±1σ.