  Galaxy power spectrum and bispectrum signals are distorted by peculiar
velocities and other relativistic effects arising from a perturbed spacetime
background. In addition, study of correlation functions of tracers in Fourier
space is often done in the plane-parallel approximation under which it is
assumed that line-of-sight (LOS) vectors are parallel. In this work we show
that a simple perturbative procedure can be employed for a fast evaluation of
beyond plane-parallel (wide-angle) corrections to the power spectrum and
bispectrum. We also show that evolution of linear matter density fluctuations
in a relativistic context can be found from a simple method. For the power
spectrum at linear level, we compare leading order wide-angle contributions to
multipoles of the galaxy power spectrum with those from non-integrated and
integrated relativistic corrections and estimate their possible contamination
on local fNL measurements to be of order a few. We also compute wide-angle
corrections in the presence of nonlinear terms at one-loop order. For the
bispectrum, we show that wide-angle effects alone, even with fully symmetric
choices of LOS, give rise to imaginary, odd-parity multipoles of the galaxy
bispectrum (dipole, octupole, etc.) which are in many cases larger than
previously known ones of relativistic origin. We calculate these contributions
and provide an estimator for measuring the leading order bispectrum dipole from
data, using a symmetric LOS definition. Finally, we calculate the leading order
corrections to multipoles of real plane-parallel bispectrum multipoles and
estimate the apparent local fNL induced to be of order unity.
