Schwarzian equations from the paper
   The Ising model: from elliptic curves to modular forms
and Calabi-Yau equations
(arxiv version here)
    A. Bostan, S. Boukraa, S. Hassani, M. van Hoeij,
J.-M. Maillard, J-A. Weil and N. Zenine

The Q series (series in z representing q) is here.
The non-linear operator for this series operator can be checked here.