  We examine the computation of wide-angle corrections to the galaxy power
spectrum including redshift-space distortions and relativistic Doppler
corrections, and also including multiple tracers with differing clustering,
magnification and evolution biases. We show that the inclusion of the
relativistic Doppler contribution, as well as radial derivative terms, are
crucial for a consistent wide-angle expansion for large-scale surveys, both in
the single and multi-tracer cases. We also give for the first time the
wide-angle cross-power spectrum associated with the Doppler
magnification-galaxy cross correlation, which has been shown to be a new way to
test general relativity. In the full-sky power spectrum, the wide-angle
expansion allows integrals over products of spherical Bessel functions to be
computed analytically as distributional functions, which are then relatively
simple to integrate over. We give for the first time a complete discussion and
new derivation of the finite part of the divergent integrals of the form
$\int_{0}^{\infty} \mathrm{d} r r^{n} j_{\ell}(k r) j_{\ell^{\prime}}(q r)$,
which are necessary to compute the wide-angle corrections when a general window
function is included. This facilitates a novel method for integrating a general
analytic function against a pair of spherical Bessel functions.
