  By applying an hyperbolic deformation to the uniformization problem for the
infinite strip, we give a method for computing the accessory parameter for the
torus with one source as an expansion in the modular parameter q. At O(q^0) we
obtain the same equation for the accessory parameter and the same value of the
semiclassical action as the one obtained from the b -> 0 limit of the quantum
one point function. The procedure can be carried over to the full O(q^2) or
even higher order corrections although the procedure becomes somewhat
complicated. Here we compute to order q^2 the correction to the weight
parameter intervening in the conformal factor and it is shown that the unwanted
contribution O(q) to the accessory parameter equation cancel exactly.
