Hodge filtrations for twisted parametrically prime divisors

We extend previous work to the case of $\mathbb{Q}$-divisors. Namely, for certain parametrically prime holomorphic functions $f$ and $\alpha \ge 0$, we obtain an explicit expression for the Hodge filtration on $\mathcal{M}(f^{-\alpha }):={\mathcal{O}}_X(\ast f)f^{-\alpha }$.