  We use the 2MASS extended source catalogue to determine angular correlation
functions, w_p, to high orders (p<=9). The main sample contains 650,745
galaxies and represents an order of magnitude increase in solid angle over
previous samples used in such analysis. The high-order correlation functions
are used to determine the projected and real space hierarchical amplitudes, s_p
and S_p. In contrast to recent results, for p<=6 these parameters are found to
be quite constant over a wide range of scales to r=40 Mpc, consistent with a
Gaussian form to the primordial distribution of density fluctuations which has
evolved under the action of gravitational instability. We test the sensitivity
of our results to the presence of rare fluctuations in the local galaxy
distribution by cutting various regions of over-density from the main sample;
unlike previous analyses, we find that our results are relatively robust to the
removal of the largest superclusters. We use our constraints on the K-band S_p
parameters in two ways. First, we examine their consistency with non-Gaussian
initial conditions; we are able to rule out strong non-Gaussianity in the
primordial density field, as might be seeded by topological defects such as
cosmic strings or global textures at the 2.5 sigma confidence level. Second, we
investigate the way in which galaxies trace the underlying mass distribution.
We find evidence for a non-zero quadratic contribution to the galaxy bias,
parameterised by c_2=0.57+/-0.33. This positive result represents a significant
difference from the negative values found previously; we examine a possible
explanation in the light of recent observations which universally provide
negative values for c_2.
