Q0}$, $w(z)$ are nonlinear. The bias parameter $b(z)$ only appears as 2nd order polynomials

 Smoothing Integrations of the Correlation Function 
----------------------------------------------------

Evaluating the correlation matrix of the equation (\[eq2-9\]) requires the six-dimensional integration of the correlation function in general. Direct integration is not a good idea. It is extremely important to obtain the elements of the correlation matrix without involving time-consuming steps such as multi-dimensional numerical integrations, because we need to construct many huge correlation matrices, with various cosmological models. We need to develop a method to calculate them with algebraic and interpolating methods without numerical integration for each element. There is actually such a method with special choices of the shape of the smoothing kernel as shown below.

The signal part of the correlation matrix of equation (\[eq2-9-1\]) is essentially the correlation function of the smoothed density contrast, $$\xi^{\rm (s)}_{ij} =
  \left\langle
    \delta^{(s)}_{R}(x_i,\theta_i,\phi_i)
    \delta^{(s)}_{R}(x_j,\theta_j,\phi_j)
  \right\rangle
\label{eq3-20}$$ where $$\delta^{\rm (s)}_{R}(x,\theta,\phi) =
  \int {S_K}^2(x') dx' \sin\theta' d\theta' d\phi'
  W_{R}(x,\theta,\phi;x',\theta',\phi')
  \delta^{\rm (s)}(x',\theta',\phi')
\label{eq3-21}$$ is the smoothed density contrast in redshift space, which is convolved by an normalized kernel function $W_R$. The normalization of the kernel is given by $$\int {S_K}^2(x') dx' \sin\theta' d\theta' d\phi'
  W_{R}(x,\theta,\phi;x',\theta',\phi') = 1.
\label{eq3-21-1}$$ The kernel function $W_R(x,\theta,\phi;x',\theta',\phi')$ 