  The Alcock-Paczynski (AP) effect is a geometrical distortion in
three-dimensional observed galaxy statistics. In anticipation of precision
cosmology based on ongoing and upcoming all-sky galaxy surveys, we build an
efficient method to compute the AP-distorted correlations of galaxy number
density and peculiar velocity fields for any larger angular scale not relying
on the conventionally used plane-parallel (PP) approximation. Here, instead of
the usual Legendre polynomial basis, the correlation functions are decomposed
using tripolar spherical harmonic basis; hence, characteristic angular
dependence due to the wide-angle AP effect can rigorously captured. By means of
this, we demonstrate the computation of the AP-distorted correlations over the
various scales. Comparing our results with the PP-limit ones, we confirm that
the errors due to the PP approximation become more remarkable as the visual
angle of separation between target galaxies, $\Theta$, enlarges, and especially
for the density auto correlation, the error exceeds $10\%$ when $\Theta \gtrsim
30^\circ$. This highlights the importance of the analysis beyond the PP
approximation.
