  Given an o-minimal expansion $\mathbb{R}_{\mathcal{A}}$ of the real ordered
field, generated by a generalized quasianalytic class $\mathcal{A}$, we
construct an explicit truncation closed ordered differential field embedding of
the Hardy field of the expansion $\mathbb{R}_{\mathcal{A},\exp}$ of
$\mathbb{R}_{\mathcal{A}}$ by the unrestricted exponential function, into the
field $\mathbb{T}$ of transseries. We use this to prove some non-definability
results. In particular, we show that the restriction to the positive half-line
of Euler's Gamma function is not definable in the structure
$\mathbb{R}_{\text{an}^{*},\exp}$, generated by all convergent generalized
power series and the exponential function, thus establishing the
non-interdefinability of the restrictions to a neighbourhood of $+\infty$ of
Euler's Gamma and of the Riemann Zeta function.
