  We study the resurgence properties of the coefficients $C_n(\tau)$ appearing
in the asymptotic expansion of the incomplete gamma function within the
transition region. Our findings reveal that the asymptotic behaviour of
$C_n(\tau)$ as $n\to +\infty$ depends on the parity of $n$. Both
$C_{2n-1}(\tau)$ and $C_{2n}(\tau)$ exhibit behaviours characterised by a
leading term accompanied by an inverse factorial series, where the coefficients
are once again $C_{2k-1}(\tau)$ and $C_{2k}(\tau)$, respectively. Our
derivation employs elementary tools and relies on the known resurgence
properties of the asymptotic expansion of the gamma function and the uniform
asymptotic expansion of the incomplete gamma function. To the best of our
knowledge, prior to this paper, there has been no investigation in the existing
literature regarding the resurgence properties of asymptotic expansions in
transition regions.
