  For any holomorphic function $f\colon X\to \mathbb{C}$ on a complex manifold
$X$, we define and study moderate growth and rapid decay objects associated to
an enhanced ind-sheaf on $X$. These will be sheaves on the real oriented
blow-up space of $X$ along $f$. We show that, in the context of the irregular
Riemann--Hilbert correspondence of D'Agnolo--Kashiwara, these objects recover
the classical de Rham complexes with moderate growth and rapid decay associated
to a holonomic $\mathcal{D}_X$-module.
  In order to prove the latter, we resolve a recent conjectural duality of
Sabbah between these de Rham complexes of holonomic $\mathcal{D}_X$-modules
with growth conditions along a normal crossing divisor by making the connection
with a classic duality result of Kashiwara--Schapira between certain
topological vector spaces. Via a standard d\'evissage argument, we then prove
Sabbah's conjecture for arbitrary divisors. As a corollary, we then recover the
well-known perfect pairing between the algebraic de Rham cohomology and rapid
decay homology associated to integrable connections on smooth varieties due to
Bloch--Esnault and Hien.
