space. There are two predominant sources for the redshift-space distortion.

The first source of the distortion is the peculiar velocities of galaxies. The peculiar velocities along the line of sight increase or decrease the observed redshift by the Doppler effect. On nonlinear scales, the peculiar velocities are dominated by the random motion in a cluster potential. On linear scales, the coherent motion along the density gradient is predominant. The linear velocity distortions are relatively simple when the distant-observer (or plane-parallel) approximation is applied. @kai87 found the linear power spectrum in redshift space, $P^{\rm (s)}({{\mbox{\boldmath $k$}}})$ is anisotropically distorted along the line of sight, and is given by the formula, $$P^{\rm (s)}({{\mbox{\boldmath $k$}}}) = (1 + \beta \mu_{{\mbox{\scriptsize\boldmath $k$}}}^2)^2 P(k),
\label{eq2-10}$$ where $P(k)$ is the power spectrum in real space, $\mu_{{\mbox{\scriptsize\boldmath $k$}}}$ is the cosine of the wavevector ${{\mbox{\boldmath $k$}}}$ to the line of sight. The counterpart of this formula for the linear two-point correlation function, $\xi^{\rm (s)}({{\mbox{\boldmath $r$}}})$, which is given by the Fourier transform of equation (\[eq2-10\]), was derived by @ham92.

The second source of the distortion is what is called Alcock-Paczyński (AP, hereafter) effect. @alc79 pointed out that the spherical objects in deep redshift region appears to be 