  We develop a perturbative expansion of quantum Liouville theory on the
pseudosphere around the background generated by heavy charges. Explicit results
are presented for the one and two point functions corresponding to the
summation of infinite classes of standard perturbative graphs. The results are
compared to the one point function and to a special case of the two point
function derived by Zamolodchikov and Zamolodchikov in the bootstrap approach,
finding complete agreement. A partial summation of the conformal block is also
obtained.
