  We present an angular power spectrum analysis of the 2MASS full release
extended source catalogue. The main sample used includes 518,576 galaxies below
an extinction-corrected magnitude of K=13.5 and limited to |b|>20. The power
spectrum results provide an estimate of the galaxy density fluctuations at
extremely large scales, r<1000 Mpc. We compare this with mock predictions
constructed from the LCDM Hubble Volume mock catalogue. We find that over the
range 1<l<100 the 2MASS C_l is steeper than that for the Hubble Volume model.
However, in the linear regime (l<30) there is good agreement between the two.
We investigate in detail the effects of possible sources of systematic error.
Converting linear power spectrum predictions for the form of the
three-dimensional matter power spectrum, P(k), and assuming a flat CDM
cosmology, a primordial n_s=1 spectrum and negligible neutrino mass, we perform
fits to the galaxy angular power spectrum at large linear scales (l<30,
corresponding to r>50 Mpc). We obtain constraints on the galaxy power spectrum
shape of Gamma=0.14+/-0.02, in good agreement with previous estimates inferred
at smaller scales. We also constrain the galaxy power spectrum normalisation to
(sigma_8 b_K)^2=1.36+/-0.10; in combination with previous constraints on
sigma_8 we infer a K-band bias of b_K=1.39+/-0.12. We are also able to provide
weak constraints on Omega_m h and Omega_b/Omega_m. These results are based on
the usual assumption that the errors derived from the Hubble Volume mocks are
applicable to all other models. If we instead assume that the error is
proportional to the C_l amplitude then the constraints weaken; for example it
becomes more difficult to reject cosmologies with lower Gamma.
