  We use polynomial truncations of the Fourier transform of the local measure
to calculate the connected q-point functions of Dyson's hierarchical model in
the broken symmetry phase. We show that accurate values of the connected 1, 2
and 3 point functions can be obtained at large volume and in a limited range of
constant external field coupled linearly to the field variable. We introduce a
new method to obtain the correct infinite volume and zero external field
extrapolations. We extract the leading critical exponents and show that they
obey the scaling and hyperscaling relations with an accuracy ranging from 10^-5
to 5 10^-3. We briefly discuss how to improve the method of calculation.
