  The hydrodynamic limit and Newtonian limit are important in the relativistic
kinetic theory. We justify rigorously the validity of the two independent
limits from the special relativistic Boltzmann equation to the classical Euler
equations without assuming any dependence between the Knudsen number
$\varepsilon$ and the light speed $\mathfrak{c}$. The convergence rates are
also obtained. This is achieved by Hilbert expansion of relativistic Boltzmann
equation. New difficulties arise when tacking the uniform in $\mathfrak{c}$ and
$\varepsilon$ estimates for the Hilbert expansion, which have been overcome by
establishing some uniform-in-$\mathfrak{c}$ estimate for relativistic Boltzmann
operators.
