Special-relativistic recession velocity uses 1 + z = √((1+β)/(1−β)). Observed wavelength is simply λ₀(1+z). The Hubble-law distance cz/H₀ is only meaningful for small z; beyond z ≈ 0.1 it diverges from a proper cosmological calculation, which needs Ωₘ, ΩΛ and an integral over the expansion history. Light-travel time here uses a flat-matter approximation, so treat values above z ≈ 1 as order-of-magnitude only.