  We derive general expressions for how the Alcock-Paczynski distortions affect
the power spectrum and the bispectrum of cosmological fields. We compute
explicit formulas for the mixing coefficients of bispectrum multipoles in the
linear approximation. The leading-order effect for the bispectrum is the
uniform dilation of all three wavevectors. The mixing coefficients depend on
the shape of the bispectrum triplet. Our results for the bispectrum multipoles
are framed in terms of the "natural" basis of the lengths of three wavevectors
but can be easily generalized for other bases and reduction schemes. Our
validation tests confirm that the linear approximation is extremely accurate
for all power spectrum multipoles. The linear approximation is accurate for the
bispectrum monopole but results in sub-percent level inaccuracies for the
bispectrum quadrupole and fails for the bispectrum hexadecapole. Our results
can be used to simplify the analysis of the bispectrum from galaxy surveys,
especially the measurement of the Baryon Acoustic Oscillation peak position.
They can be used to replace numeric schemes with exact analytic formulae.
