  We apply the formalism of spherical harmonic decomposition to the galaxy
density field of the IRAS PSCz redshift survey. The PSCz redshift survey has
almost all-sky coverage and includes IRAS galaxies to a flux limit of 0.6 Jy.
Using maximum likelihood methods to examine (to first order) the distortion of
the galaxy pattern due to redshift coordinates, we have measured the parameter
\beta= \Omega^{0.6}/b. We also simultaneously measure (a) the undistorted
amplitude of perturbations in the galaxy distribution when a parameterised
power spectrum is assumed, or (b) the shape and amplitude of the real-space
power spectrum if the band-power in a set of passbands is measured in a step-
wise fashion. These methods are extensively tested on a series of CDM, \Lambda
CDM and MDM simulations and are found to be unbiased. We obtain consistent
results for the subset of the PSCz catalogue with flux above 0.75 Jy but
inclusion of galaxies to the formal flux limit of the catalogue gives
variations which are larger than our internal errors. For the 0.75 Jy catalogue
we find, in the case of a parameterised power spectrum, \beta=0.58\pm0.26 and
the amplitude of the real space power measured at wavenumber k=0.1 h/Mpc is
\Delta_{0.1}=0.42 \pm 0.03. Freeing the shape of the power spectrum we find
that \beta=0.47\pm 0.16 (conditional error), and \Delta_{0.1}=0.47 \pm 0.03.
The shape of the real-space power spectrum is consistent with a \Gamma= 0.2
CDM-like shape parameter, but does not strongly rule out a number of other
models. Finally by combining our estimate of the amplitude of galaxy clustering
and the distortion parameter we find the amplitude of mass fluctuations on a
scale k=0.1 \hmpc is \Delta_\rho = 0.24 \Omega_0^{-0.6}$, with an uncertainty
of 50%.
