The peculiar velocities of galaxies cause their redshift-space clustering to depend on the angle to the line-of-sight, providing a key test of gravitational physics on cosmological scales. These effects may be described using a multipole expansion of the clustering measurements. Focussing on Fourier-space statistics, we present a new analysis of the effect of the survey window function, and the variation of the line-of-sight across a survey, on the modelling of power spectrum multipoles. We determine the joint covariance of the Fourier-space multipoles in a Gaussian approximation, and indicate how these techniques may be extended to studies of overlapping galaxy populations via multipole cross-power spectra. We apply our methodology to one of the widest-area galaxy redshift surveys currently available, the 6-degree Field Galaxy Survey, deducing a normalized growth rate f*sigma_8(z=0.06) = 0.38 +/- 0.12 in the low-redshift Universe, in agreement with previous analyses of this dataset using different techniques. Our framework should be useful for processing future wide-angle galaxy redshift surveys.
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