  Assuming General Relativity is correct on large-scales, Redshift-Space
Distortions (RSDs) and the Integrated Sachs-Wolfe effect (ISW) are both
sensitive to the time derivative of the linear growth function. We investigate
the extent to which these probes provide complementary or redundant information
when they are combined to constrain the evolution of the linear velocity power
spectrum, often quantified by the function $f(z)\sigma_8(z)$, where $f$ is the
logarithmic derivative of $\sigma_8$ with respect to $(1+z)$. Using a spherical
Fourier-Bessel (SFB) expansion for galaxy number counts and a spherical
harmonic expansion for the CMB anisotropy, we compute the covariance matrices
of the signals for a large galaxy redshift survey combined with a CMB survey
like Planck. The SFB basis allows accurate ISW estimates by avoiding the
plane-parallel approximation, and it retains RSD information that is otherwise
lost when projecting angular clustering onto redshift shells. It also allows
straightforward calculations of covariance with the CMB. We find that the
correlation between the ISW and RSD signals are low since the probes are
sensitive to different modes. For our default surveys, on large scales ($k<0.05
\Mpc/h$), the ISW can improve constraints on $f\sigma_8$ by more than 10%
compared to using RSDs alone. In the future, when precision RSD measurements
are available on smaller scales, the cosmological constraints from ISW
measurements will not be competitive; however, they will remain a useful
consistency test for possible systematic contamination and alternative models
of gravity.
