  We use a variety of series expansion methods at both zero and finite
temperature to study an antiferromagnetic Heisenberg spin model proposed
recently by Miyahara and Ueda for the quasi two-dimensional material
SrCu$_2$(BO$_3$)$_2$. We confirm that this model exhibits a first-order quantum
phase transition at T=0 between a gapped dimer phase and a gapless N\'eel phase
when the ratio $x=J'/J$ of nearest and next-nearest neighbour interactions is
varied, and locate the transition at $x_c=0.691(6)$. Using longer series we are
able to give more accurate estimates of the model parameters by fitting to the
high temperature susceptibility data.
