Comparing the Lorentz transformations in terms of the relative velocity and rapidity, or using the above formulae, the connections between β, γ, and ζ are β β = tanh ⁡ ⁡ ζ ζ , γ γ = cosh ⁡ ⁡ ζ ζ , β β γ γ = sinh ⁡ ⁡ ζ ζ .