the formula of the redshift-space distortions. Accordingly, the Runge-Kutta integrations of the set of equations (\[eq3-8a\]) and (\[eq3-8b\]) meet the requirement.

The linear formula for the two-point correlation function in redshift space is presented in Appendix \[app2\]. It has the form, $$\xi^{\rm (s)}(z_i,z_j,\theta_{ij}) = 
  b_i b_j D_i D_j
  \sum_{n=0}^2 \sum_{l=0}^{2n}
  c_l^{(n)}(x_i,x_j,\theta_{ij}) \xi_l^{(n)}(x_{ij}),
\label{eq3-10}$$ where $z_i$ and $z_j$ are the redshifts of the two-points and $\theta_{ij}$ is the angle between them. The linear bias parameter $b(z)$ as a function of the redshift is introduced. The distances $x_i
= x(z_i)$, $x_j = x(z_j)$ are comoving distances to the two points according to equation (\[eq3-4\]). The comoving separation $x_{ij}$ between the two points is calculated by equation (\[eqa3-19\]). The functions $c_l^{(n)}$ are given by geometrical quantities and defined by equations (\[eqa3-20a\])–(\[eqa3-20i\]). The functions $\xi_l^{(n)}$ are given by integrations of the power spectrum, and defined by equation (\[eqa3-17\]). Although the expression (\[eq3-10\]) is somewhat long, it is straightforwardly calculated once the single-variable functions $f(z)$, $D(z)$, $x(z)$, $b(z)$, $\xi_l^{(n)}(x)$ are calculated and tabulated beforehand for a fixed cosmological model.

While the correlation function linearly depends on the power spectrum through the function $\xi_l^{(n)}(x)$, the dependences on other cosmological parameters like ${{\mit \Omega}}_{\rm M0}$, ${{\mit \Omega}}_{\rm 