Ramanujan-type series for 1/π , revisited

In this note, we revisit Ramanujan-type series for 1/pi and show how they arise from genus zero subgroups of SL2(R) that are commensurable with SL2(Z) . As illustrations, we reproduce a striking formula of Ramanujan for 1/pi and a recent result of Cooper et al., as well as derive a new rational Ramanujan-type series for 1/pi . As a byproduct, we obtain a Clausen-type formula in some general sense and reproduce a Clausen-type quadratic transformation formula closely related to the aforementioned formula of Ramanujan.