  We study the perturbative series associated to bi-local correlators in
Jackiw-Teitelboim (JT) gravity, for positive weight $\lambda$ of the matter CFT
operators. Starting from the known exact expression, derived by CFT and gauge
theoretical methods, we reproduce the Schwarzian semiclassical expansion beyond
leading order. The computation is done for arbitrary temperature and finite
boundary distances, in the case of disk and trumpet topologies. A formula
presenting the perturbative result (for $\lambda \in \mathbb{N}/2$) at any
given order in terms of generalized Apostol-Bernoulli polynomials is also
obtained. The limit of zero temperature is then considered, obtaining a compact
expression that allows to discuss the asymptotic behaviour of the perturbative
series. Finally we highlight the possibility to express the exact result as
particular combinations of Mordell integrals.
