  The most commonly used estimators of the anisotropic galaxy power spectrum
employ Fast Fourier transforms, and rely on a specific choice of the
line-of-sight that breaks the symmetry between the galaxy pair. This leads to
wide-angle effects, including the presence of odd power spectrum multipoles
like the dipole ($\ell = 1$) and octopole ($\ell = 3$). In Fourier-space these
wide-angle effects also couple to the survey window function. We present a
self-consistent framework extending the commonly used window function treatment
to include the wide-angle effects. We show that our framework can successfully
model the wide-angle effects in the BOSS DR12 dataset. We present estimators
for the odd power spectrum multipoles and, detect these multipoles in BOSS DR12
with high significance. Understanding the impact of the wide-angle effects on
the power spectrum multipoles is essential for many cosmological observables
like primordial non-Gaussianity and the detection of General Relativistic
effects and represents a potential systematic for measurements of Baryon
Acoustic Oscillations and redshift-space distortions.
