= Hubble parameter for matter and dynamical dark energy
Assume spatial flatness, negligible radiation, separately conserved <pressureless matter> and <dark energy>, and $a_0=1$. Let $w(z)=P_{\rm DE}/\rho_{\rm DE}$ be the dark-energy <equation-of-state parameter>. The <cosmological continuity equation> gives
$$
\rho_{\rm DE}(z)=\rho_{{\rm DE},0}(1+z)^3
\exp\left(3\int_0^z\frac{w(z')}{1+z'}\,dz'\right).
$$
Combining this with $\rho_m=\rho_{m,0}(1+z)^3$ in the <Friedmann equation> yields
$$
H(z)=H_0\left[\Omega_{m,0}(1+z)^3
+\Omega_{{\rm DE},0}(1+z)^3
\exp\left(3\int_0^z\frac{w(z')}{1+z'}\,dz'\right)\right]^{1/2},
$$
with $\Omega_{m,0}+\Omega_{{\rm DE},0}=1$. For $w=-1$, the dark-energy factor is constant and this reduces to the matter-plus-<cosmological constant> model. Nonzero <cosmological spatial curvature>, radiation or energy exchange between the components requires additional terms or modified continuity equations.
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