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.